{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Conjugate Gradient Method"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import scipy.optimize as sopt\n",
        "import matplotlib.pyplot as pt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let's make up a random linear system with an SPD $A$:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "np.random.seed(25)\n",
        "n = 2\n",
        "Q = la.qr(np.random.randn(n, n))[0]\n",
        "A = Q @ (np.diag(np.random.rand(n)) @ Q.T)\n",
        "\n",
        "b = np.random.randn(n)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Here's the objective function for CG:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def phi(xvec):\n",
        "    x, y = xvec\n",
        "    return 0.5*(A[0,0]*x*x + 2*A[1,0]*x*y +  A[1,1]*y*y) - x*b[0] - y*b[1]\n",
        "\n",
        "def dphi(xvec):\n",
        "    x, y = xvec\n",
        "    return np.array([\n",
        "            A[0,0]*x + A[0,1]*y - b[0],\n",
        "            A[1,0]*x + A[1,1]*y - b[1]\n",
        "        ])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Here's the function $\\phi$ as a \"contour plot\":"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.contour.QuadContourSet at 0x7fc6d591b780>"
            ]
          },
          "execution_count": 75,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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UoU9IELBhgxo7dmgwaJAlFiywwvPPlyy8LyFBi/37c/DLLznIyNBj3LgGGDeuAby9rctt\nBSkAaDQGJCZqkJCgRmKiGgkJaiQna5CRoUVGhu7fP7XIz9ejoMAAjUZAnToWsLau8e/VtMYVtQqF\nAgYDoVYLUKsNUKsFWFoqYGdnCXt7S9jb14K9vSWcnWvBzc0Kbm7WcHOzQtOm1mjWzBqWluW/BoAk\njh7Nw+LFyWjZsja+/dYFrVtbmaXtLVvUWL5chWPHbOHjI/1a0mqNA5ZevYyDF7EIAtB3BDDuVeDD\naZK7rfTIgl8JUKmAL74Dtuw2LhmfMx2oVav4euHhwKJFwN27wIoVxpS0UkY10dEGrF6tgq+vDm+/\nXQtz5ljB3d30YZFaLeD333OxY0c27t9XYfTo+pg4sQF697Yp85F8WpoGDx7kIzg4H0+fFiI8XImI\niEKkpGjg4mKFJk2Mh6trbbi41IaTUy04OhoPBwdL1KtXEzY2FrC2thBlO0loNAJycvTIytIiK0uH\nzEwdUlI0iI9XIz5ejbg4FWJjVUhK0qBZM2u0bVsXHTrYomvX+ujZswHs7UWc9FJAqxWwaVMmvvoq\nDdOm2WP5cmdYWZX8gXTypBaTJxfC17cuevWSvlArPR3w9jauFRkzRny90HDgheHAg8tA40aSu63U\nyIJfwfG/Brw3D3i+A/D9F+Iu0Lw8YNUq48rYhQuNi1esJAzM4uIM+OILNX77TYuZM2tj7lwr2Nub\nfoOHh2uwZUsm9uzJxvPPW2PqVHuMGFHPLKIhhsRENW7dysHt27m4fz8PDx7kQ6MR0LGjLdq1s0Xr\n1jZo2bIOWra0QdOmVqhZs3xH12q1AeHhSoSEFODhw3zcvp2DW7dy0LSpNV54wQ4vvGCPAQMc0LBh\nMbk0zExqqg4zZyYiLEyLQ4eaom3bko/2z57V4u23C3HtWj20bCl9MHHnDjB8OPDoEeAkYQfs+UuN\nC7s2SHg7qArIC68qKFnZ5JTZpFtHY+pXMRgMxtA1Fxdy8mQyOVlan0lJBs6cWUB7+yx++mkhMzJM\nn1jT6QT6+uZw4MBIOjkFc/HiJEZFlX50jVZr4K1b2Vy3LpKjRt2lq+tFOjqe59Chd7h8eRiPH09h\nbKzS7OGHpY1OZ+CdOzn89tsojhwZxHr1zrF795v84osIPniQW2afRxAEbtuWQUfHYB4+LCKMTARb\nt6rYsmW2ydfb/PnkpEnS6iSnkPYtySSJ90hlB3KUTsVCEMhDR0mX58gPF5O5eeLq3blDdu9OenuT\nt25J6zMjw8CFCwtpb5/F+fMLmZZmutBnZOi4Zk0q3dxC2KNHOPfty6JaXXqrXLVaA2/cyOLKleEc\nMOAW69Y9y/btr/GDD4L5yy+JjIwsrHTiLga1Ws9z59I5e/ZjNmt2ic2aXeKSJU/59GlBmfQfFFRI\nD48Qzp+fSJ2u5N/vokWF7N07lyqV9Lby842Lsq5ckVbvw8Xk4hWSu6vUyIJfwUhLJ30GkTdEinZG\nBvnee8YFKTt2SFs0lZ8vcMUK46KYGTMKmJBgujA/fKjktGnxrF//Ed96K4537vzDzidmIiysgBs3\nRnPEiCDWr3+OHTte47x5ITx+PIWZmdUvRl8QBP7xRw7nzg1ho0YX6e19g5s2xTArq3RXHGdk6Dh4\ncBT79IkocaoGg0Hg66/nc/x40xZ/HT5MPvec+A1/SDI61jjKz5EY3lmZkQW/AiLmehcEcv9+4yKU\nDz8ksyW8XRsMAnfvVrNx4yyOH5/PiAjTl73fvl3I4cOj2KjRY65cmcKUFPOLjCAIvHcvl59//pRe\nXlfZuPFFTpnykL/+msjUVBPyP1RhdDoDT59O4xtv3KODw3kuXRrG7OzSE369XuDnnyfT0/NJic+9\nUimwU6cc7twp/ZwKgnEB4bZt0uqNm0b+8C/J3VVaZMGvhMTFGbcQbNeODAyUVvfWLR19fHLo7Z3D\nwEDTV8XeuFHAwYOj2KRJCDdtSqdSaV63jSAIfPAglx9/HMrmzS+xefNLXLDgCQMCssy+CrSqEhlZ\nyHfeeUBHx/NcvTqceXmll4JixYoUduz4lNnZJcuZExSko7Nzlkn+fH9/44JCKW+5x8+QfYZL7qrS\nIgt+JUIQyK1bSUdHcuVKaXlBUlIMfOedfLq4ZHHXLrXJonn9egEHDIikh0cIt27NMLt/PiKigCtX\nhrNt2yt0d7/ExYtD+ccf5l3xWd14+rSA48ffY6NGF7lzZ3ypPDAFQeDs2Qns1SuchYUluyZmzy7g\ntGnS5yIEwZj8z89PfB212riPc2I1mbyVBb+SEBlJ9u9PdutGBktI9arTCdywQUVHR+OEbG6uaTd7\nQEABX345ku7uIfz55wyzpjrIztZy69ZY9ux5k05OF/jhh49544Y8kjc3t29ns2vXG+zVK4D375vf\ncW0wCJw0KZZDhkRRozFd9HNzBbq6ZvH6dekuov37yb59pdV5aya5UaIrqLIiC34FRxCMuUMcHMh1\n68RlzvyTGze0bN8+h/375/LxY9NetR8+VHLIkCi6uYVwy5aMEt3If0UQBF6+nMFx4+6xXr1zHD36\nLo8fT6FWW/3y1pcler3ArVtj6eR0gXPnhlClMm9qZK1W4PDhUZwwIbZEb2WHDmnYrl0O9XppbWi1\nxogdKRk1T5wle78i0cBKiiz4FZi0NHLYMLJrVzI0VHy9ggKBs2cX0MUliwcOqE268dLSdJwxI54N\nGz7mxo3pZnPdqFR67tgRz44dr7FNmyvctCmmWkbWlDfp6RqOGnWXvXsHMCPDvN+/Umlg+/ZPuW9f\nlsltCILA7t1zeOSIdNuWLjXG5otFqSSt3Yw/qzqy4FdQLlwgXV3JRYuk+eovX9ayefNsTpyYb1JG\nQo3GwPXr0+joGMyPPkpkZqZ5JvpSU9VcujSMzs4XOHjwbZ4+nSa7bMoZg0HgwoVP2KrVFUZEmDd+\n/9atQjo7P2Z6uunXz8GDar7wgnTX0927pKentHTfz/cnb96W3FWlwxTBl1MrlCI6HbB0KbBnD7Br\nlzFBlBgKCoiPP1bi6FEtNm+2wfDh0vOunDmTj48+SkSLFsZEWW3alHzpfFhYIdavj8ahQ8kYO9YF\nc+d6oE2buiVu15yoVHrExRUgJqYAsbEFSEtTIT1djYwMNdLT1cjJ0UKl0v87CZrxUCiAmjVrwNLS\neFhZWcDevjYcHGrD0dEKDg610aSJDVq0qIcWLerBw6MuatWqmOkZN2+OxcqVkfD17Yzu3e3M1u7c\nuUnIyjJg9243k+rr9USLFrn4/fe66NpVfII1EnBzAy5cANq0EVdnxgLAqxUw+z2TTK00mJJaofR2\nQZZBXh6QkmLcQFxsbpArV3SYPLkQffvWxKNH9WFnJy0XTGSkBvPmJSMkRI3vv2+MV14peSrcwMBs\nrFkThZs3c/D++03x9GmfMs/98ndSUpQIDs5GSEg2QkJyEBKSg/DwXGRlaeDmVhceHnXh7l4XjRpZ\nw8OjLrp1c4SjoxXs7GrD2toCVlY1YW1tgdq1jcKt0wn/OVQqPbKyNMjMNB4ZGWoEB2fj2LFYREXl\nIyGhEE2a2KBzZwd07eqErl0d0aWLI+zsyvc7AYD333dH06bWGD78LrZubYfXXjNPRrFVq5zRrl0Y\nzp/Px8CBtpLr16ypwMyZtfHTT2rs2CF+kKBQAEOHAqdPixd8786A/3XJJlYL5BF+BUGnI5YuVWHP\nHg22brXBsGHSRvU6HbFuXTq+/TYdCxY4Ye5cR9SuXbLEYffv5+HTT8Pw+HE+Fi5sjilTmqBOnbIf\n2RoMAh49ysaNG6m4fj0FN26korBQj/bt7eDlZQcvrwbw8rJDq1b14eJiDQuL0k2YptMJiIrKw927\nGQgKMh737mWiTZv6GDu2OV5/vRk8PKSLojm5ezcXw4bdxe7d7fHyyxIykRXByZN5mD8/GSEhrUzK\niJqeLqBFixykptrB2lp8/d9/B3bsAE6eFFf+QTAwfgbwuIqLvpw8rZISE6Nnjx65HDIkj6mp0n31\nDx4o2bnzU778ciRjYko+aRceXsA33jDGem/aFGO2aB4pREXlccuWEI4efZ52dnvYuvUhTp16hTt2\nPGVYWMWL5dfpDDx/PoHvvnuVjo576e19lOvXP2RGhqrcbPL3z2CjRheZmGgeGwRBYKdOT3nypOlh\noD165PL8eWkhmmFhpLu7+PKZWWSDFtLsqoxAnrStfPj6aujklMV165SSJz61WoErVqTQ0TGY27dn\nllgE09LU/OCDYDo4nOeqVeHMzy+7DcW1WgP9/RM5Z04APT0P0tl5HydM8Ofu3WFMTCybJGLmQqs1\n8OzZeL711mU2aLCb06df45Mn5slGKZWVK8PZp08AdTrzPLR37szkoEGRJtdfsqSQn3wiLTeTTkda\nWZEFIi8DQSBrNSZV5fesLRNkwa9EaDQC58wpoIdHtklpEe7fV7JTp6ccMiSqxBuBK5V6fvllBB0c\nznPWrMdMSyubnDaFhToeOhTJ8eP9aWe3h127+nLlyj94715GhRvBm0pyciGXLQuis/M+Dhlympcu\nJZZp/3q9wAEDbvHTT5+apT2VykBn58d88sQ0NfX319LbW+SmzX+hfXtjxI5YmnQgY+Ikd1OpkAW/\nkhAbq6e3dw5HjMiTHG6p1wv84otUOjkFc8eOko3qBUHg/v2JdHPz5+jRdxkWVvojaZ3OwJMn4/jm\nm/6sX383Bww4yc2bQ5iQULlG8VJRqXTcvj2UzZsf4ODBp/n0qXTRM5XUVDVdXS/y7Nk0s7S3dGky\n338/waS6KpXAunUzmZMj7bofO5bct098+a4DyIA7Eo2rZMiCXwm4dk1LF5csrl0rfeOOlBQtBwyI\nZN++EYyLK9moPjq6kIMG3WbHjtd4/brpi2rEkpxcyBUr7tLVdT+9vY/yxx8fMzW1GqyO+RsajZ7f\nfvuQjo57uXt3WJn1e+JEKr28rpplvUR4uJqNGz82ebDh7Z3Dmzel+fHnzTOuThdL3xGk/zWJhlUy\nTBH88t9duRqxa5cGr71WgO3bbbBwobQNvi9fLsDzz4eje/c6uHChOdzcTNsT1WAgvv8+Gl273kS/\nfva4c6cnevUyX7z2XyGJgIBUjB9/CW3b/oakJCVOnx6MW7dGYuZMLzRsaF0q/VZkatWywNy57eHv\nPxRr1jzApEmXUVioK/V+hw51Qt26Fvjtt5QSt9WiRS0YDEBsrGl2N21aA3FxgqQ6deoY94MWi14P\nWMpB5/+DLPhlgCAQixcrsWqVCleu1MOQIeLFWhCIL75IxZtvxmHnTjesWtUINWuatkn448f56Nkz\nAEePpuHmzR74+OMWsLQ0/yWg1ws4cCAS3bodw6RJV9CtmyOio8dhy5beaN/e3uz9VUbat7dHUNCr\nAID+/U8hPV2CmpmAQqHAp5+2wDffRP/5Zl2itnr3tsGNG4Um1W/a1MIkwVcqxZfX6YGasuD/D7Lg\nlzIFBcRrrxUgMFCPW7fqoW1b8XHsWVl6jBgRg1On8hEU1BIvv2xabLdeL+DLLyPRr98tTJnSBP7+\n3mjVysaktooiP1+L778PhqfnIWze/ARLl3ZGWNjrmDu3PRo0KP9FSRWNOnVqYs+evhg40BU9e/oh\nMjKvVPsbNqwhsrN1uHkzp8Rt9epVB9evmyr4po3wpQi+Xhb8f0QW/FIkPV1Anz55sLdX4Px5Wzg6\niv+6Q0LU6NYtAq1a1cblyy3g6mppkg1RUUr07BmIK1eycPduL0yf3tSkRTNFoVbr8fXXD9Cs2UEE\nBKTi0KH+uHJlGEaMcDd7X1UNhUKB1au7Yv789ujT5wQSE00TUTFYWCgwe7Y7fvoptsRt9expg8BA\nCQr8F1xdayAxUZrg164NqNXiy2u0QC3TbpkqjSz4pYiNjXE5+fbtNqhVS7zwXbiQj379IrFsmTO+\n/bYxLC1NE83ffktG9+4BmDixMc6c6YqmTc3rMyeJAwci0abNbwgMTMPNmyNw8OBL8PZuaNZ+qgMz\nZrTFjBltMXHiZRgM0sRQCq+80hCXL2eV2K3TpIklUlP1JtWtUcOYI0cKublAPQlZQhKTgcbmySpR\npZBfekqROnUUmDZNWtKynTuz8PHHKTh82B19+5qWmEyrFbBoUSiOH0/DqVNd0bVrfZPaKYqbN1Mx\nb14g9Ho87s/AAAAgAElEQVRi9+6+6NvXxex9VDc+/bQjLl1KwpdfPsDnn3culT6aNbOGIAAxMSo0\na1bH5Hbs7S2QlWUASUnBB4AxDYjUQUxmJuDoKK5sXj6g1QEO8nTR/yALfgWBJFasSMWePTm4cqW5\nydkt4+JUGDfuPho2rIW7d3vBzs6877VJSYVYvPgOLl1KwldfdcOECZ6y28ZMWFjUwN69/dCpky9G\nj/aAl5f5o6eME652uHEju0SCb21dAwoFoFIRdepIO/96PWAp8bLMyABatRJXNjYecG9iTLwm8/+R\nXToVAJ2OmDw5AadO5SMgoIXJYn/uXDq8vW9i1ChnHD36vFnFXqcTsG7dQ3TocARubjYIDX0dkya1\nlMXezLi62mDZss6YPv16id0uz6JXrwa4fj27xO0YR/nS3To6nfQJVSkj/LgEo+DL/C/yCL+c0WoF\nvPFGHDQa4tKlFrCxMe0Z/K9/xePzz8Nx8GAn9O3rYFYbQ0NzMGnSZdjZ1UZAwAi0bGl+F5HMf3n/\n/bbYuPEx7txJL5X5kPbtbXH8eFqJ27G0VECrlf5Qys4m6teXNlCIjQVcXcWVDQkDWrWQbFa1QB7h\nlyNarYDXX4+DIAC+vu4mib3RFRSOr76KxLVrPmYVe5L4+edQ9O7th8mTW+Hs2cGy2JcBFhY1MGZM\nMxw9WvJomn+iTh0LqFQlnxjOzDTA0VH6mDEy0gBPT/HhyVotEBYGtGsnrnxgENC9q2SzqgWy4JcT\nf4p9jRrAoUNNUauW9FOh1wuYPv0xjh83LqTy9DRfbH1WlhpjxlzEjz+G4Nq1YZg500vy5JyM6bz6\nqjt8fWNKpW1rawsolYYStaHRCNBoCFtb6ddteLgBnp7i64WGAu7ugLWIIDMSCAgCuneRbFa1QBb8\nckCrFTB2bBwUCuDgQdPEXqk0YPToe4iJUeLyZR84O5tvYdPly0no1MkX7u51cevWSLRtWzqpF2Se\nTdeuTsjP1yE0tOSLpP6OtXUNqFQlE/zMTAMcHCxMGgRERAiSRvgPHgAdO4orm5AEGATAo6lks6oF\nsuCXMQYDMX58PADTR/aFhXoMGnQH9erVxIkTXWFra56pGJL45puHGD/+MrZt641vv+3+ny0AZcqW\nGjUUGD68KU6ejDN727Vr14BaXTKXTnq63iR3jkZDJCYK8PAQf93fuyde8G/eBnyelyN0noU8aVvG\nzJuXhKwsPU6fbmaS2Gs0Bowa9Qc8Petg+/b2ZouSEQRi3rxAXLyYhNu3R6JJE/OnXpCRhru7LdLT\nJSwvFUlysgYuLiV7I7x/X4V27aS3ERioR8eOFpIWIp4/D/z8s7iyJ84Dg/tLNqvaUOqCr1AoYgDk\nAhAA6Eh6l3afFZWNGzNw4UIBbtzwNGm/Wb1ewJtvPkC9ejXx88/tzCb2Go0Bb711GSkpKly7NkzO\ne1NBsLKygFpdMtfLPxEeroSnp+kx+ABw+7YK3t7S2/D316F/f/HhwnFxQEoK0K1b8WV1OuDkeeCr\nJZLNqjaUhUtHANCPZOfqLPZ+fnlYsyYNJ082Q4MG0t0kgkBMmxaMwkID9u/viJo1zXPqcnO1GDz4\nDAQBOHt2sCz2FYjSEvyIiMIST/Dfvq00UfD1ePFF8YJ/8iQweDBgIeKWuRYIeDYDmjSWbFa1oSwE\nX1FG/VRY7t1TYcqUePj6esDDQ3oee5KYO/cJIiKUOHKks9n86qmpSvTtewLt2tnhwIEXYWVVOT18\nJJGQkIeQkHRkZCghCKWzYKmssba2KPHk6j8REVGyEb5aLSAkRI3nn5eWm6mwkLh3T49evcRfZydP\nAq+8Iq7s0VPAyMGSTKp2lMUdTgBnFQoFAWwjKdIbVzXIztZj1KgY/PSTK3x8TLvJNm+Ow6VLWbh6\n1Qc2NuY5Zfn5WgwefBbDhzfFypVdKlXIZVRUNo4ff4qHD1MREpKOkJB01KljCTs7a6SlFSIvTwMH\nB2s0bmyLSZM6YPr0rqhTp/KlTiwo0Js0z1Mcd+/mYeHCZibXv3atEO3bW8PaWpptZ8/q4ONTEzY2\n4q61rCzg+nVg797iy+p0wG9+gL+vJJOqHWUh+D1JpigUCicA5xUKxROS1/9aYPny5f/5vV+/fujX\nr18ZmFX6kMTUqQkYObIeXn+9gUlt3LqVg+XLIxAQ0B0NGphHtHQ6AWPGXIS3t1OlEfuoqGwcPvwY\nhw+HID4+DyNHtkb37k0wZUpntG3rCAeH/z5MdToD0tOViIzMwoYNt/D11zcwb14PzJzZDXXrmrZT\nWHkQFJSO7t3Nu9I2LKwQ+fl6dOwoIfXk39i/PwdvvCF9Ad6uXRpMmiTeZbhvHzB0KGAnIirY7yzQ\nwgNo01KyWZWGy5cv4/LlyyVrROqeiCU5ACwDMO9v/2aO7R0rJMHBKvbsGU61WtqGzX+Snq5h06b+\n9PVNMZtNgiBwypQrfOWVM9TpTLOrrNDrDTxyJIS9e+9gw4brOGOGHy9ejJJs96NHqRw37jCdnNby\np59ul5K15sfL6zD/+CPdrG2uXx/Fd999ZHJ9pdLABg2CmZQkbU/a5GQDGzTIYn6+uH1wBYFs1470\n9xfX/qDXyT0HJZlU6UFF28QcQB0Adf/9uw2AGwBe/luZ0vtGKgCmbhqt1wscNOg2Fy58YlZ7Vqy4\nyy5dfJmfL+2GLUsKC7X86afb9PTcyG7dtvHgwWCzPJweP05jy5YbuX79TTNYWbrk5mpoY7OTWq15\nH8r9+gXy+HHTBxCHDmVzwIBIyfXWrVNy8uR80eUDA8kWLUiDiI8fGU06tCKVSslmVWpMEfzSduk4\nA/D9t/++JoD9JM+Vcp8VClNDJ9esiYRKZcCXX4rMCSuCw4ejsHNnGAICRqBu3Yrp0/bze4pp0/zQ\no0cT7NgxAr17NzWby8nLywkXL76Fvn13wcOjAV57ra1Z2i0Nbt1KQ8eO9mbdczgzU4u7d3Px0ksi\n007+A3v3ZmP8eGnuSZLYsUODLVvERwZt2wZMnWrcLKU4tuwG3h4nLvVCdadUBZ9kNIBOpdlHVSQ0\ntADffReDe/d6mS38Mj1dhVmzAuDn9zIaNSpZDHZpceJEGKZN88OxY2+ge/fSyW/r5lYfI0e2RkyM\n+VMWmJNdu8Lx2mseZm1z8+Y4jB7dCHXqmBblFRqqRmCgEr/+6i6p3okTOtSqpcALL4iTm4QEwNcX\nePq0+LKZWcD2/cDdC5JMqrZU63DJighJzJjxGEuXesLNzXxDlrlzAzFxoie6dXMyW5vm5MyZCEyZ\ncgx+fm+Wmtj/SVJSAVxcTNtNrCxISVHi1Kl4TJnS2mxtKpUGbNoUi0WLmpvcxtdfp2PWLEdJWV1J\nYvVqFZYssRb9prZuHTBlCuAk4lL9bgvw2ity7hyxVM7A6yrMvn1JyM/X44MPpI2iiuL06XgEBKTh\n4cPXzNamOTl/PhJvveWLY8fegLe3yKTnJSA5OR+NG9uWej+m8vPPTzF2bHPY2ZlvEdyOHQno2dMO\nbdua9qCLi9Pi+PE8RERIewhduKBHfj7x2mviXIgpKcYwzMePiy+blQ1s3gUEnZdkUrVGFvwKRHa2\nDosWPcWxY8/DwsI8fuv8fC1mzLiB7dtfgI1NxfPbX74cgwkTjuDIkXHo0cOtTPpMSqq4gq/TCdiy\n5QlOnx5k1ja/+SYaBw+a7l395pt0TJ1qDzs7aZKxerUKn31mLXoua/16YPx4wEXEFsnfbQFGDQWa\nmW9sVOWRBb8CsXZtFIYNc4K3t2kx+//E+vWP0LdvIwwYUPojZ1P44INT2L7dODlbFly6FI3cXA2a\nNDE9Dr002br1Cdq0aYAOHcy3kc3PP8fD07MOfHxMu66io7XYvz8HwcHSAgjOntUiOVnAuHHi1j7E\nxQE7dhjTIRdHSqpxdH/7rCSTZKSG9Zj7QBUPyxRLTo6W9vbnGRVVaLY2VSodGzbcyydPss3Wprmp\nW/dL5uSoyqSve/eS6eS0lpcuRZdJf1KJjs6jg8Mes56v5GQ1HR3PMzg4z+Q2Ro6M5urV0kI5NRqB\nrVpl089PI7rO66+Ty5eLKzt5FrlQZNmqCipgWKaMSLZujcegQY5o1sx8ETS//BKJLl0c0aaN+d4Y\nzElBgRYGg4B69Uo/Ydvdu0kYOvQXbN78Cvr18yj1/qRCEu++ew0LFnQw6/lauDAUU6Y0wXPPmebC\nOnEiDyEhahw4IO0N7Lvv1GjZ0gLDhokb3V+8CNy5A+zeXXzZoPvAGX8gNECSSTKAPMKvCKjVerq4\nXOT9+7lma1MQBHbo8DvPno03W5vmJiwsg82bbyj1fgID49mw4Tr6+pp3EZs5+fnnJ+zSxdesq5/9\n/TPYtKk/8/N1JtUvLDTQwyOE585JezuIi9PTwSGLERF6UeW1WrJtW9LXt/iyBgPpM4jcsV+SSVUS\nmDDCl8MyKwD79iWhY0fbEuU3+Ts3bqRCozFUWN89AGRlqaDXl3wz7WdBEr6+TzB8+K/Yvn0EXn21\nTan1VRJiYvLxySdB2Lmzj9nWXahUBsyc+RgbNnihbl3TXuRXr06Fj08dDBwo/u2AJObMUeLDD2uj\nRQtx8f4bNwJNmwIjRxZfdtevxp9vv1F0uch4IDtPVPfVC6lPCHMfkEf47N//llnz5ZDk558H8dNP\nK3beGLVax+bNN3DlysvUasWNBsWg0xn422+P2avXdrZr9xOvXIkxW9vmJjdXw3btfuN335me3+bv\nCILAyZMf8I037lEQTEvtceVKPhs1eszkZGkpOPbtU7Nt22wqleL6DQ0lHRzIsLDiyyYkkU5tyD8e\nFF1OoyU7jCb3nRBlQqUFFS2XjigDqrngZ2ZqaGt7loWF5hM8khw8+DSPHq24QvcnsbE5HDRoLzt2\n3MygoMQStZWaWsDVq6+wSZNv2bv3Dh448Ih6fcVNEKfVGjh48GnOmHHNZGH+J7Zti6OX11WTXTmZ\nmTq6uYXw5ElpLsaYGD2dnLJ49664fnU60seH/OGH4ssKAjlkHLl8bfFlP/+BHP6hsU5VRhb8Ssje\nvQkcMSLIrG0KgkAHhz1MTCwwa7ulhSAI3LPnPhs2XMeFC8+xsFD8qDIhIZdbtwZxxIhf2aDBGk6b\ndoz37iWXorXmQRAETp16hUOGnDZrgrTbt7Pp5HSBoaHiE5X93a5Ro6I5Z460h69eL7Bv31yuWSM+\ng9nKleSAAeISpP1rL9n5RaO/vyiCHpNOfcikNNFmVFpMEXw5SqecOX48DSNHmjfneUxMAWrXtkDj\nxpVjI3KFQoFJkzpi0CBPzJ59Gq1abULv3k3Rvn1DdOjgjA4dnFGnjiUSE/ORkJCHxMQ8REVl4+zZ\nSMTH52HQoBYYO9YLu3aNhJ1d5cigtWrVPdy/n4XLl18xW4K0jAwtxoy5h61bn0Pr1qatqN2yJQvR\n0Vr8+qu0qJz169UQBGDBAitR5e/cAX74Afjjj+ITpMUlAB+vBvyPAJZFrB3UaIF3lgDfLQJcKmYG\nkXJHYXxQlKMBCgXL24bygiTs7S8gJOQFuLiIu1HEcOJEHH78MQSnT1fO/d5CQtJx714yHj5MxcOH\naXjwIAUajQGurrZwda0HV1dbNG1aH/37N0P37k3MNtFZVqxb9xBbtjzBzZvD4exsnjBclcqAwYPv\noEcPO6xZY1oOnps3CzFyZAxu3PBEq1biQ2WvX9fhtdcKcPt2PXh4FD9Rm5tr3JR81Spg3Liiy+r1\nwIDRwKAXgU/mFF124XogPA7w/R6oBHv6lBiFQgGSkj6pPMIvRzIytKhRQ2FWsQeMKZkr8wXv5eUE\nLy8nTJhQ3paYF5JYtOg2Tp2Kx9Wrw8wm9jqdgHHj7sPV1crkdNqRkRqMHh2LPXvcJIl9XJwBY8cW\nYO9eG1FiLwjAW28BAwcWL/YAsORLoFYtYNGsosudvAocPAv8cbB6iL2pyIJfjkREKNGihflTFVtZ\nWUCtNv/m1zKmo9Ua8O671/H0aQ6uXRsGe3vzPOQNBuLttx+CJHbv7mDS/gtZWXq88koMli51xpAh\n4kODCwuJkSMLsGCBFQYNErfA6quvgPR04PDh4ssePQX86mtMfWxRxLMkPgWYugz4bT3gKGI7xOqM\nLPjlSGSkEp6esuBXdfLytBgz5iKsrCxw8eJQsyWxI4kZM4KRkqLByZNdTZoL0GgEjBoVi2HDbPH+\n++Lz9wgC8c47BejY0QJz54p7eJ09C/z4o9F/X6uY50NEFPDefMBvH+BYhFlaHTB2ATBvEtD7edHm\nV1sql/OzilGaI3yVShb8ikB8fAH69DmB5s1tceTIALOK/bx5oXj0KB/HjnWBtbX0TU0EgZg2LQEO\nDhZYu1ZEesq/sGqVGgkJArZssRGV5z4y0ujKOXAAcC1mLaBSCYyeAixfCPh0Kbrsx98DDg2ABe+I\nt706I4/wy5G8PD1cXc3rvwcAd/e6iIrKg1qth5WVfIrLixMn4jB16lUsWNABCxa0N9tWjQaDcWR/\n/34+zp7tCltb6edYEIjp0xMRE6PF2bPNJbmCtm1TY/duDW7cqAcrq+LrpacDQ4YAK1YAffoUZxcw\ncSbQuR3w/uSiy+4+Bhy7BNz+RdxWiDKy4Jcr1talMxJ3cLBCx44O8PdPxtChZZNjXua/qFR6LF58\nG8eOxeHIkQHo1auR2dpWKg148837UKkM8Pf3Nlns33svAWFhWpw+3Qx16ohXy19/1WDlShWuXKkH\nF5fi6xUWAsOGAWPHAjNmFN/+4pXGbQt/3Vr05OuNe8DCb4HLO4wjfBlxyM/FcsTaugZUqtLJJTNi\nRFMcOxZbKm3LPJtHj7Lg7X0Mqakq3L8/yqxin5GhxUsv3Ua9ejVx4oTpI/t3301AeLgWp055oG5d\n8a6g48e1mDtXibNnbUXlydHrjZE4Xl7GEMzi+GkH4HcW8N0N1C4iUCgmERgzH9i9GvBqIdp8GciC\nX65YWdUotcnVkSPd4ecXB0GonmscyhqS2LgxGP37n8L8+e1x4EB/s25RGB2tRK9egejXzx579nRA\nrVrSb90/ffYREVqcPClN7C9e1GHatEL4+dniueeKf9CQwPTpgMEAbNtWfKjkiXPAqvXAqV8B+yIi\nbfIKgOGzgMWTgSEvPLtc0FMgNbtYM6sdsuCXI/b2lkhP15ZK2y1b1oeTkxXOnEkolfZl/ktwcBYG\nDDiNffsiERAwHO+808ps/noAuHYtC716BWLWLHd89VVrk9rWaARMnBiPqCgtTp1qJknsr1zR4Y03\nCnD4cF106yZO7D/+2Lhz1eHDRa+OBYCAO8Dk2cDRPUBzj2eX0+qA1xcAvTsDH018drnwBGD4UuBR\ndLGmVj+k5mIw94FqnEsnMDCbnTpdK7X2/fxi6eHxK3Nzxe86JCOejAwVZ868Tienvfzhh8dmzWVP\nGvParF0byYYNL/DUKdOTw2Rm6vjCCxEcPTqGSqU0G0+e1NDRMYsXLojLbyQI5MKFZKdOZEZG8eX/\neGDMgHnqfNHl9Hpy3ELy1Y+MSdeeRXIm2XwS+fNJUeZWaiAnT6tcaDQG2ticZV6eaVkNxfDee9c4\nefKVUmu/OqLVGrhxYzCdnPbyww9vMCPD/Fs0ZmVpOWJEEH18bjA2VnxCsr8TGalm69ahXLAgkQaD\ntPSRBw6o2bBhFm/eFC/2CxaQnTuLE/vHoWQjL/J3v+Lbnb6SfHEKqVI/u1xuAdlpOrlyryhzKz2y\n4FdCevcO4Pnz6aXWfn6+li1aHOTvv0eVWh/VBUEQ+PvvUWzZ8iAHDjzFR48yS6WfoKAcNmt2iR99\n9JgajelvDQEBBWzU6DF//FH69bVtm4qNG2fxwQNxgxFBIOfPN4p9poiv5WkE2bgdue9w8WU/3UB2\nGUfmFpEAVK0hX1pIzvi+6qdF/hNZ8CshixY94fLlInZ/KAE3b6bQ2XlfpUmXXBG5fj2ZvXodL9Vt\nIw0GgRs3RtPJ6QIPH04qUVuHDmXT0TGYfn7SctoLgsB165R0d89mWJi4PRoEgZw3T7zYR0aTbh3J\n7fuKL7tuJ9l6OJlWRLt6PfnGavK15cbfqwuy4FdCLl/OYOvWV6jXl+6wZO3aB2zZ8iBjYqTtT1qd\nMRgEHjsWwz59/Nis2QHu3Pm01DZUCQ8vYN++gfTxucHwcNMfzFqtwHnzEunuHsI//pDmCtJqBc6c\nWUAvrxzGxYnfj/add0hvb3Fi/yTMKPabdxZf9ptdZPMhZHwR2xsYDOQ7a8l+80llEe6eqogs+JUQ\nQRDo43ODv/1W+pt2bNjwiE2a/MKbN827nWJVo6BAyx9/fExPz4Ps1u0oDxyIMPuE7J/o9QLXr4+i\ng8N5rl8fVaIHf3y8hj17hnPo0ChmZEibF8rKMnDAgFwOHpzHnBxxnzU/nxwyhBw6lCwQ8Yy699Do\ns9/1a/Flv/oX6flK8WI/9Ruyz1yywPRpjkqLLPiVlKNHU/j889fNus3dszh2LIZOTnu5YcOjMumv\nMhERkcsFCwLp6LiXo0ad4/XryaX6HT18mEcfnxvs2zewRKN6kjx3Lo+NGj3ml1+mSp6cDQvTs1Wr\nbM6ZU0CdTlzd1FSya1dyypSio2b+5Hog2bAtefhY8WVXbjG6cRJTn13GYCDf+47sPYfMr4ZiT8qC\nX2kxGAQ+99xVnjlTNvuyRUTkslOnIxw37iLz86VtUl3V0OsNPH48hoMHn6aj414uXBjIyEhpfm+p\nKJV6fvJJKJ2cLnDr1ljJAv1XdDqBn36azMaNH9PfX/q2hhcvatmwYRa3bRMfaRQRQXp6kkuWiJsg\nPX2BdGxNnrlYdDlBIJf+QLYdSSYXMc8sCOT7G8ges8m8QtFmVzlkwa/E7NuXQB+fG6Xuy/8TpVLH\nqVOvsFWrQzx+PKZEolPZEASBgYGpXLAgkG5uv9Db+yh37w6jUll64bF/9nv8eAo9PS9z7Ng/mJRU\nsnDOiAg1e/UK58CBkUxJkfbgFgSB336rorNzFi9dEl/36lWyUSNy82Zx5ff/ZhzZ37hVdDmDgZy3\njuwwmkwtIqTTYDBG4vh8aAzDfBbH75GxIkJDKzOy4Fdi9HqB/fvf4ooVpRux83eOHYth585H2K7d\nb9y7N8ysG2pXJHQ6A69cSeLcuQF0c/uFrVod4mef3eGDB2WjCkFBOezf/xbbtLnC06dL9iYnCAJ/\n+imDDg7B/OabNMkP68xMA0eMyGO3bjmMihIf1rJ5M+nkRJ4+LcZGctU3ZNNO5KOQostqtOT4xWSv\nt8jMnKLLvbGa7DuvaLHfd5NsNIe8H1u8nZUZWfArOYmJKjo7X+C1a6UT3/0sBEHgmTPx7NfvBN3d\nf+XGjcHMyqr8IQ+ZmSru3x/ON9/0p53dHnbufIRLlwbx4cPMMpu/iIoq5Pjx9+jicpFbtsSWePI3\nKkrD/v0j2a1bGENCpL8hBATo6O5u9NdrNOK+A42GfO890suLDBMxHlGrybc/ILu8RCYVE4uQm08O\neNe4glZZxMcpVJFDPiGHLyk6GmfbZdJ1Hvk4oXg7Kzuy4FcB/PxS2bSpPzMyyicdQkBAKl9//QLr\n1dvF0aPP8+jRGGo0lSO4uaBAyzNn4rlo0S126eJLW9tdHDHiLLdte8KEhLJdg5CeruHcuSG0tz/P\n5cvDmJ9fMneRwSBw06Z0OjgE8+uvU0VPrv61/rp1SjZsmMWjR8VfW0lJZK9e5MiRZJ6IiN70DPKF\nYeSot4uP3ElOJzu/blxFW1T8fHY+2esjctIaUlvE1/j9OdJ9ARleTYLQZMGvIixc+IQvvhhYru6V\nrCw1t259wt69j9PRcS+nTbvKw4ejmJJSMWbJBEFgZGQuDxyI4Ny5AezR4xhtbHbyhRf8uGxZEK9e\nTS6XB1V2tpZLl4bR3v48Z84MZnJyyd+UwsPV7NMngj16hPPJE+mj+pQUAwcNymPPnrmMiRH/ndy4\nQbq6ksuXG33nxREaTrboSi5eUXz5kEjSY5AxIqeol63kTLLje+TsH57dpiCQX/iRnovJmNJbtF7h\nMEXwFcZ65YdCoWB521DRMBiI0aP/gE5HHDrUCTY25btPTVRUHo4fj8P584m4eTMVdna14ePjhPbt\n7dG6dX20adMAnp71ULu29G32ioIksrM1iI8vRFRUPkJDc/D0aS5CQ3MQGpoLW1tLdOniiO7dG6J7\ndyd06+Zkti0EpZKaqsH338dg27Z4DB/eEMuWeaJZs5JtX1lQYMCXX6Zh27YsfPZZQ8ye7QgLC2mZ\nMg8f1mLWrEJMm1Yby5dbo2bN4usLAvDNN8D69cD27cYNTIrj+Blg2lxgzRJgyoSiy569AUz6FFg3\nD3h75LPLBUcDwz4Hpg4Glkz45xTLBgGYdwC4+AQ4Nw9oXI02MVcoFCAp6YKQBb+CotMJePfdYISG\nFuDkya5wcChm1+cyQhCIsLBcBAam4cmTnP+IcExMARo1skajRtZwdrZGo0Z14OxsDVtbS1hbW8DK\nygLW1jVRq1YN6HQC9HpCpxOg0wnIz9chO1uDrCwNsrM1yMjQICGhEAkJhbC0rIEmTWzQrFldtGnT\nAG3aNPjPQ8bR0fzbQ0rlyZMCfPttNH77LQVvvtkYixY1g4dHyYSeJH75JQeLF6fgxRdtsGaNC1xd\npT3IMjIEfPihEvfv67FrV1107y5u0JCaCrz9NpCfD/zyC+DuXnR5vR5YugbY9xtw6F9A967PLksC\n3+0F1u0CDn9T9KbjZ+8Ak9YC380AJrz0z2VUWmDSz0BmIeD7IdDA/NtDV2hkwa9ikMQnn4Th6NFU\nnD3bDe7u1uVt0jPR6QTExxcgNVWFlBQVUlKUSE1VoaBAD5VKD7XaAJXKAK3WAEvLGrC0rIGaNY0/\nbW0tYWdXC/b2tWFnVxv29rXRpIkN3NxsYGtbMR50f4UkLl/Owvr10bhzJxcffNAU77/fFE5OJd/w\nJChIiTlzkqBWExs3NkbPnjaSbTt8WIuPPlJi/PjaWL3aGtbW4jThzBlgyhRg8mTj/rM1i3lGpKUD\nb4GXyTcAACAASURBVE43jrx/3Qo4OT67rFoDvL8auBcKHNsAuDd+dtktfsDyvcDhz4EX2v9zmcwC\nYORGwM0e2DUVqF0+L3bliimCL/vwKwHffx9NF5eLvHKlbKN3ZP4/hYV6bt0ay/btr7FNmyvcti2O\nSqV55gni4zWcNCmWLi6P+a9/ZZq0LiI52cDXXstjmzbZDAgQP0msVpNz55JubuSlS+LqBNwx5sT5\ndHXxCcsSU0nvN8nX55MFRUwB6fXkvM1kq3fI8CKibKLTydafkIsOPduvn5BDaitHrIHJQJ60rbqc\nOZPGhg0v8IsvIqpsrHxFJTg4j/PmhdDB4TyHDw/iuXPpZgvrzM7Wc8mSZNrbB/PTT5OZlyddpQwG\ngTt2GHPXf/xxIVUq8bY9fGjcrGTUKHHJzwwG8tvNxk1Ljp8pvvy1u2Tjl8gvthU9OZtTQA5bQr64\ngMwsYqFzQATpMofcdOHZZf5IJF2/Is+V7ZKWMkcW/CpOTIySQ4bc4XPPXeX161nlbU6VJiVFze++\ni+Lzz19n48YX+fHHoYyMNF+EUm6unqtWpdDRMZjvvBPHmBjTwnDv3NHRxyeH3t45DAoSP6rXaMgV\nK0hHR/Jf/xKXIiExmRw4huwxxJjiuCgMBnLtDrJhX/Lk1aLLBkeTLd8mP9hYdNjlruuk4yzjKtpn\ncSyEdFpNHn5YdJ9VAVnwqwGCIPDgwSS6uFzkhAn3GRVVMcIkqwK5uVru2ZPAIUPusH79c3zrrQc8\nfz7drOku/ir0EyfGMjTUtPQKaWkGTptWwEaNsrhjh1qSCygoiOzQwZjlMi5OXJ0jJ0jntuTytcUn\nS8vIJl/5gPQZT8YWk9b/0GXScTS5+9yzy+gN5PwDZIvFz15QJQjkN1fJxl+Rt0tnu4IKhyz4FZDC\nwtJxv+Tl6bhsmTHee9asx0xNrfwrY8uDggIdDx5M4qhRd1mv3jkOG3aH+/YlsKDAvHl1srP1XLmy\n5EKv1QrcsEFFJ6cszplTIDqVMUmqVOTHH5MNG5J79ogb1eflk1M/Ipt3JW/eLr789T9It4Hk/HXG\nVAjP/Bw6cv4W0mMiebcI10tWATl4PfnSWjLzGbnhtHry3SNkhw1kbHbxNlYVZMGvYERHa9i0aYjJ\nN7cYUlPV/D/2zjs6yqrr4r/03hNIgYQk9BJ6rwIiCCJiFxULKthQX7Dy2bGi2BFEwQJYQJAOSpMm\nvYSekIT0OkkmZfqc748bJCQzSUBBSvZad90J3Jk8M0n2Pc+5++zz5JOHJTDwd5ky5bjk5tYTf23I\nyzPInDlpcuONu8XHZ40MGbJTvvkmTTSaf985NDfXJC+8kCmBgYdk7NjUf/S7sHq1QVq1KpRrry2W\nQ4fObUPauFGkeXORm28Wya5jJeqWvxTR3/+EIv6aYLEoD/sG/UWWbax5bVaB8rAf+kLN+frD6SLN\nnhd5cp6Iyc7RRn6ZyIBZIiO+FdFeZb/69YR/CWLOnAIJDT0/69pzQVJSmYwbd1D8/NbKzTfvkeXL\ncy5Y047LDXq9WTZuzJeXXz4hPXpsEx+fNTJ69B757rt0KSi4MBYW8fE6efjhNPH3PyTjx6dJUtL5\nf589e0xy7bXF0rRpoSxdajinA+OsLJF77lEVs7/+WrfnlJaKPD1FNStZvKL29alZIgMfVOZnqbV4\n56zdLRJ2m8gr39ZcjbvgL5Wvn7PZ/pr9mSIx74tMXqnSPlcb6gn/EsW6dSXSsOFhmT4994KbdhUW\nGuXLL09J9+5bJTx8nUyceFg2bsy/aLbLlwL0erNs2aKRd95JlCFDdoqPzxrp2nWrPPfcMfn99zzR\n6y+MXs9kssqvvxbJNdckSljYYXn11exzti2ujEOHTHLzzVoJC9PIF1/oxGis+8/QaBSZPl0dyk6e\nXDcfHBGRPzapqH7MeOWLUxOsVpFvfxMJ6Sfy1lc15/YNRpHnvhKJuENk3V776/RGkce+V/n6vSn2\n1/2wTyT4DZEF++1f25WOesK/hJGcbJAOHY7L3XefkpKSiyMQPnKkRF577YR06LBZQkL+kAceOChL\nl2ZLcfGV1fQkI0MnS5Zky/PPH5M+fbaLl9ca6dx5izz55GFZvDj7gqRqKiMnxyRvv50jkZFHpGfP\nBJk/XyMGw/mHnImJZrn77hIJCdHIe++VS1nZubHX778rZ8vBg0WO1GJNfBoFGpW6adxeZNma2tfn\nFojc9JRIu9Ei+4/VvDYhXaTLoyLDXxLJrSHHfjJHpMtrIjd9KlJkR4tgMIk8uVQk9n2Rg3buJgp0\nIkMWi/xRxwPpyxWXJOEDQ4FjwAngORv/f8E+kEsNZWUWGTs2VZo1Oyq7dl1cdU1ycplMn54kAwfu\nEG/vNdKt21Z59tmjsmpV7mWzAVgsVklKKpMlS7Ll9dcTZOTI3RIWtk6Cgn6XoUN3yssvn5Dff88T\nrfbCNjIRUWqpTZtK5I47UsTf/5A88ECq7N79z36myclmGTeuVIKCNPLaa+VSXHxuRJ+UpPT00dEi\nixfXLcq1WkV+/FUkrI3IE8/XnqsXEVm8TiRsoMhz00X0NWSqrFaRuWuUCueTWq5n0W6RkCdFPl5r\nf11GsUivGSpfr7HT1vBgnkjMHJH//SlypWc0z4fwL6i1goODg2MF0Q8CMoFdwB0icqzSGrmQ13Ap\n4qefinjiiQyeeCKYZ58Nwc3N8aJ+f73ewo4dRWzcqGHDBg27dxcTFuZG585+xMX50KaNN7GxnkRF\neeDjc3GN26xWIT/fSHKyjqSk8oqh4+jRUg4dKsHX15m4OF/atfOmc2c/unb1o0kTDxxsOWtdAGRk\nmFiwoIg5czSIwPjxQdx7bwD+/udvHHfypIV339WzaJGRCRPceOYZdwID6/47UVwM770HM2fC00/D\n//4H7nWwGUpKgYkvQXIqfPUh9Oxa8/r8QnjqPdgRD3PfgN4d7a8tLIHHPoUDSbDgRYiLsb1Ob4Jn\nf4blB+CnCdA12va6DSdhzM/wWA94oT842vh4fkmARzfAR/1gTMua38uVgEvOS8fBwaEH8IqIDKv4\n+nnUrvRupTVXHeEDpKUZefzxTI4c0fPhh+GMGOFz0UirKiwW4fjxUvbs0RIfX8Lhw6WkpOhISdHh\n4eFIkyYeNGrkTkiI61nDx8cZT08nPD2d8PJyws3NEQeHM66GDg4OGI1WdDoLOp2ay8osFBaaKoYZ\njcZITo6RrCwDmZl6srMNeHs7Ex3tQUyMJzExnkRHe9CypRft2vkQGHjxvXWKiiwsWlTMvHmF7N+v\nZ/RoX+69N4C+fb3+0c9s924z06bpWbfOxPjxbjz1lDtBQXUnep0OPvsM3n9fOVq+/jo0alT788rK\n4O2P4ctv4ZnxMOkxcK3hYxWBH5bD5A/hruvhjcfAqwajsuV/wfiP4abe8O448LSz+cSnw5hZ0CIU\nZo2FABu2QWYLvLkBZu2Cb2+Ba5tVX2O0wOQtsCwZfrkeOjeo+f1fKbgUCf9m4DoRebji67uBbiLy\nZKU1VyXhn8aqVVomT87Cz8+Jt94KpX9/7//6kv6GiJCXZyQlRUdGhp68PONZo7TUQnm5IvHycgt6\nvZXTP0p1Cwmuro54eDji4eGEh4cjnp5OBAS4EBjoQkCAGg0buhIe7k5YmBthYW64u/+7NsvnA63W\nwtKlWn7+uYiNG8sYPNibMWMCGD7cB3f3878js1qFFStMTJumJyXFysSJbjz0kDs+PnX/uzWZYO5c\nZXDWvTu8+Sa0alX780TgpyUw+VXo1xPefRka1WBiBnAyTZme5Wrgq1ega1v7awtL4KkZsOUQfP0/\nGNDe9jqrFaavhXdWwnu3wn19bFsfpxWpqN7VCb6/FcJ8q69J0cLtqyDUE+ZeCwH/vYHqRcP5EP6F\nvl+3dTHV2P3VV1/9+/GAAQMYMGDAhbuiSwzDhvkyZIgP8+cXcf/96TRv7srUqaF07vzfe706ODjQ\noIEbDRr8cxfIywFFRRaWL9eyaFEx69eX0q+fF7fd5s/330fi5/fPNqGyMuH77w189JEeLy8HJk1y\n55ZbXHFxqfvfq8UCP/4Ir76qbIt//RW6davbc/ccgKdegtIy5WzZp0fN640mmDYXPvwenrsfnrob\nXGpwpFyxAx75SEX1B2aCtx1j1zQNjJ0NRjPsmAIxdqLxxYdh/BJ4ug8829d2CmdpEjy0Dp7tDM90\ntL1pXEnYuHEjGzdu/Gcvcq5J/3MZQA9gdaWvn6fKwS1X0aFtbTAYLPL553kSFnZYhg1LkvXrSy5a\n79WrFZmZRpkxI1+GDDkpPj7xMnJkssyZUyCFhf+OkurUKbM8+2yZBAVpZORIraxfbzznn6nVKrJo\nkUibNiI9e4qsX1/352Zmidz3uNLUf/Vd7c6WIsrwrPUokesfFUmupTdsfrHI3W+LxNwjssGORPL0\ne5i3XR3MTl1mXzdfbhSZsEQk+j2R7XaakBvNIpM2i0R+I7LNjnXDca2Irt4t8+KqdAAnIBGIAlyB\n/UCrKmsu4EdyeUKns8isWfnSvPlRadfuuHzySZ5oNBdeeXI1oLzcImvXamXSpAyJizsu/v6H5K67\nTskvvxT+a3JZs9kqK1YYZNQorQQEKAuExMRzf22TSWTBApH27UU6dhRZsaLu+vJircgr74oENhN5\n9jX1dW3IyBG590XlbvnLmpq/l9Uq8v3vIqG3iTz1hUipHdWMiEhmoZJatnpRZHey/XW70kRafShy\n+3yRIjsFyQmFIt1/FBm2RCTPxve0WkXmJokELxbZnGv/e10JuOQIX10TQ4HjQALwvI3/v2AfyOUO\ni8Uqf/yhldtvTxEfn3i58cZkWbCgUEpLr3C92b8Ivd4if/5ZKq+/ni0DB54Ub+946d07QV57LVu2\nby8952bgNSEpySxTppRJRIRGunUrkpkzdVJScu6vr9OJzJghEhMj0qePyLJldSf68nKRD74QadBK\n5O4JIsl2ouSznqMTeXOmSFBfkec/EtHW0nz8eJrIoMkiHR4R2XHU/jqrVeSbP1VU/9IiEZ0d9a/B\nJPJ/a0UavKkKqWy9V6tVZPYhkeCZIh/vE7HlFac1iozZLtJqpcjBq8BT55Ik/FovoJ7w64TCQrPM\nnVsgQ4cmia9vvNx2W4rMn6+RgoL6yL8yCgvNsmqVVqZMyZJrrkkUb+946dLlhEyalCErVhRLcfG/\ne59fWmqVb7/Vy8CBxRIcrJGJE0vl4MHz+5loNCJvvSUSGioyYoTI5hpsBarCaBSZ9Z1IoziRG+8R\nia9DwZXVKvLzGtVMfPRTIidrcZks14tMmSMSNFrkw4X2/W1EVJOSIdNEOr4isq+GTedglkiHT0SG\nzxXJtOOrk1cuctNykbh5IofsVP/uLhBpulzkoZ0iZVfJn0Q94V8lyMszyaxZ+TJyZLL4+sZLr14J\n8uab2bJnT9lVZaFgMFhk9+4y+fLLfHnwwVRp2/a4eHvHy4ABifLii1myYkWxFBX9+4lci8UqGzYY\n5b77SsTfXyMjRmjll18Motef32efnCwycaJIQIDI2LEi8fF1f67ZLPL9zyJNu4pcM0p1oqoLdsaL\n9LlXpP0tIhvq4IK54i+R6LtFbntDJD2vhuuxiHy4RiToCZG3l9v3tzeZRaZuUPYIX++yfwezKlkk\nYrbK2ettvJbFKvL+UZGQxSI/1eFu5krC+RB+fU/byxx6vZXNm8tYubKENWtKyMw00auXF337etGj\nhycdOrgTEHBxi6f+bYgIOTlmDh/Wc/iwgfh4PQcO6Dh8WE90tCtdu3rSpYsH3bp50qGDxzkpX87l\nGvbutfDTT0YWLDASGOjA2LGu3HWXG6Gh5y7TFIHt2+HTT2HtWnjwQZg4ESIi6vZ8iwUWLoXXpkGA\nH7zxAgzsW/vzTmXClM9g3Q5483EYOxKcahAgJWfB/2ZCfDJ8/gQMqaFJ+YFUeOhb8HJTuvpmDW2v\nO5QN9y8Cfw/4ejRE+ldfU2aCZ7fA8hSYMxgGNq6+JksH9+2EUhPM6wlNzq3972WPS06HX6cLuIIJ\nX6cTJkwoY8IEd7p3vzikm5dnZsuWMjZvLmPnznIOHNDj5+dE27ZutG3rTps27jRt6kZsrCuhoc44\nOl4aWjaTScjIMJGaaiQlxURiooGEBAOJiUYSEgw4OTnQpo07bdq40a6dO3FxHnTo4I6394XT7Fut\nwl9/mVmyxMTChUacnODWW1256y5X2rY9v59naSnMmwczZkB5OUyYoMje14bG3BaMRpi/CN75BAL8\n4ZVJcN3A2iWJOQXw9mz4fjk8ejs8ez/41ECQ2jJ4awF8tRKeGg2TbwN3O8VZxeXwyhJYsBOmjoYH\n+9q+Hr1JFVHN3AlTh8BDXW2v25gOD/4BvcPhk/7gb0MV/HMqPLEXJjSFKa3Bucqem2aAUBdwubhF\n7BcV9YR/icFgEL76ysC0aXpiYhx5/nkPrr3W+aJW1FqtQmqqifh4PYcO6Tl8WE9SkpGTJ41otRai\no12JjHQhLMyFsDBnQkNdCA11JjDQCT8/J/z91ezj44ibm0OtG4SIYDQKOp2g01nRai0UFVkpLLRQ\nVGRBozGTk2MmO/vMnJ5uIjfXTGioM5GRLkRFudK0qStNm7rRrJmag4KcLsrnptcL69ebWLLExNKl\nRho0cGTUKBdGj3alffvzv4YDB2DWLFiwAAYMUEQ/aJBtfbktlJbC7B/ggxnQshk8/6SK6Gu7nEIt\nvD8HZi6EMcPhxXEQGmx/vdkCX6+CV76DYV1h6v0Qbme9CHy/DZ5fCMPbw9s3Q7CP7bUbTsL436BN\nA/hsJITb2OBKjPD8VvgtCb4cCCNs2CxoDPD4XthbCN91h25B1a9pfj48nQy/toQ+ddxIL0fUE/4l\nCpNJ+PFHI++8o8fNDZ54wp3bb3fF0/O/ja5LSy0kJRlJTzeRnW0mK8tEVpYi4aIiy9+juNhCSYkV\ng0FwdgY3N0X+oP7ArFZBBMxmQa8XHB2pqK51xM/PEX9/JwICnP6eQ0OdadjQpWJ2plEjF8LDXXB2\n/m8+j8xMKytWGFm+3MTGjWbi4pwYNcqFUaNciY09/zuI0lL46SdF9FlZKpJ/8MG62R+cRl4+fP4N\nfDEH+veE556ELh1qf15JGXwyDz6aBzcOgP97BKJqqKoVgdW7YPJXEOQD0ydAJxs2BqexPxUe/wEM\nZvj8buhmxysnvwwmrYL1J+HTG+DG1rbXrT0FD69XqZsP+tiumF2RCQ/vhtsaw9R24FnlJqvQDI8m\nwcEymNccOlzhKZ7zIfz6Q9uLCIvFKsuXG+T667USFKSRZ54pkxMnLp/qEKvVKgaDRbRas+TlmSQv\nzyQFBSbRaExSWGgWrdb8r8ocLxQMBqusX2+U558vk44diyQgQCN33FEiP/ygl/z8fyZ5tVpFtm0T\nGTdOHcLeeKPSz9el4KkyEk6KTJgsEtBU5KGnRY4n1u15pWUi736tOk/d+azI8eTan7M/UWTwsyLN\n7xP5bWvNEtD8EpFHvxNpMFFk5gb7BVRWq8i3e0QaThWZuMx+NyqNTuT+30WivhFZk2J7TbFR5MEd\nIk2WiWzIsb1mfZFI410iTyaJlF8+f1L/CNSrdC4fJCWZ5bnnyiQkRCP9+hXLxx/rJC2tXl9/IWAw\nWGXbNqO88065DBumFV9fjXTtWiRTppTJn38a/5VNKilJ5I03RFq0UK0E33lHJCPj3F7DahVZ96fI\nTWNFgluIvDRVJNsOwVWFtlQRfeg1IrdNEjmUUPtzTmaK3PuuSINbRD5bYl9RI6K08h+vVZr6R79T\nxG8PBzJF+s8S6fipKqayBatV5MfjIuGzRR7bIKK1Y7O8MlMkaqmSW2pt6PhLzSITk0TCd4ms1ti/\npisR50P49Smd/xgGg7B2rYlFi4wsW2aiWTNHbr7ZleHDXWnVyvE/c9C8nKHRWNmxw8z27Wa2bDGz\na5eZZs2c6NvXmX79XBgwwPmcXCntISMDfvlF+ducPAm33gr33AM9epybr4u2BL79UaVtnJzgsQfg\n3tvAqw4pidwC+GS+ytEP7g4vPQRta0jFAKTlwpvzYdFmeGwk/O8W8LXzvUTgt33w7C8QEwLv3wbt\n7KSkNOXw8h/wSzy8NlgdyjrZ+JgTipSNcU45zLhGHc5We196eHofbC+AL7vAkNDqazYVw4MnoacP\nfNwEAmvw+rkSUZ/SucxhNFpl7VqjjB9fKlFRhdK4caGMG1cqCxcapLCwPvq3hfJyq/z1l0k+/1wn\nY8eWSIsWheLjUyADBxbLiy+WycqVBikq+vc+u8xMkc8/F+nfX6Vs7rtPZPVqVfh0rtgfLzJ+kkrb\n3PagyKZa0imVkZwu8thUkYDeIuNfF0msQ3enrAKRJz8TCbxJtRvMr6GBuIjI9kSRPm+JtJ0isrqG\n2gCTWeSL7apS9tElIgV2+sDoTCIvbxcJmikybY/yxKmK09YIDRaLTNonUmrjrqPELPL4SZGIXSJL\nC6r/v8VqlS+KrZJ6GaQX/wmoj/CvHIgIJ05YWb3axJo1JjZvNhETo6LUvn2d6dPHhYiIK1hzZgMF\nBVbi4y0cOGDhwAEze/ZYSEiw0KKFE507O9O1qxM9ezrTpo0TTk7/3p1Rerpyply4EOLjlff8LbfA\n0KHgdo5GouXlyqJ45neQmQ3j7lYj3EYEawv7jsL7c2HNNnj4Fpg4pmbVDUBOIbz3E8xZC/cOhhfu\nhIYB9tcn5MCLi+Cvk/DGTXBPL9uROqjD2KdWQKAHfDwC2ofZXrcyBZ7cBO2DVYOSxjbUPIklMGEP\nFBhgdlfoFFh9zR9F8PBJ6OsLH0VD1RKTVLPwQB6UWmFeA4i9ADUZlwrqVTpXMEwmYd8+C5s3m9i8\nWaUq3Nygc2dnOnd2pmNHJ9q2dSIqyvFfJbuLDatVyMwUEhIsHD9u4dgxC8eOWTl0yExJCbRr50Rc\nnBqdOjkTF+eEu/u/+35FFLEvXQq//QZJSXDDDSplM3jwuZO8COyPh2/mw/xfoWcXGH8fDBtUc9HT\naVitsHYbTPsWjqcokn/oZvCzI4E8jZxCmPYLfLMaxgyC52+3L7EEyCqCqcvhx50w6Tp4cjB42nmv\nJwtg8irYlwXThsHoNrbTWClaePpPOFQAn/aHoU2qrzFaYNpx+PA4vNAKJjavrqsvMsPkFFhbBF/G\nwrAqG5aIMKcEntPA//xhkh84X+Hp0HrCv4ogIqSkWNm718KePWb27bNw+LCF3Fwr0dGONGvmRLNm\nTkRHO9K48ZkRHOzwn50LiAiFhUJmppWMDCsZGepxaqqVlBQLyclW0tKs+Ps70Ly5E82bO9GqlSMt\nWzrRurUTTZpcuDONoiJYtw7WrIHVq5X3+4gRMGoU9O0LzudRZ5WZDfMWwnc/Kx/6sbfDA3dBZB1l\nmcUl8N0y+PxHcHeDZ+6BO4aBay256uQs+GAhzN8Ad12jIvqIGog+VwvvroQ5W2FsL3hxOITY0a/n\nlcLUjfDDfnimDzzTG9xtXE+pEd7dA1/Ew1MdYHIncLfxGa7Lgcf2QKw3fN65erWsCPxcoHT1owLh\nnSjwrfI6ySbhkXwosMDcBtDO9com+tOoJ/xLECIXtzFDeblw8qSFhAQrCQkWUlIUiaanq7msTAgO\ndiAkxJGQEDUHBDjg6+uAj8+Z4eYGLi4OuLqq9ndOTg5YrWc6WVmtqupTrxf0ejWXlwtarVBcfGbW\naIS8PCE/30pBgeDl5UB4uCPh4Q5ERDgSFuZIVJQjTZo40qSJE5GRjhelPsFohJ07FcmvXasi+t69\n4brr1GjZ8vx+bsVa+HU5zFsEew/CzSPUAWzv7nUvsjqUoEj+pzVwbU947Hbo27n26zlwEt77Gdbs\nhoevhydvglAbaZHTyC+BD9bArE1wZ3d4YThE2En1lBlh+hb4aBvcGQdTroGGNu4wrALfHYUp26F/\nI3inl+30TWoZTDoAuzTwcUe4Ibz6+zuph8eSIMMIs2LV4WxlmEX4uBjeLoJn/eGZqyCqr4x6wr/E\nUFoK7dqpdMAddyj1Rl3/6C8UdDohL89KXt6ZuahIKCk5exiNYDSemc1mde0ODuDo6ICDg0ptuLs7\n4O6uZg8P8PNTm4evrwN+fo4EBTn8vcEEBTng+h9FX2Yz7N8PGzcqkt+6FZo1g4EDYcgQFcXXpfG3\nLeh0sPIPWPAr/L5JVcCOuRmGXwsedjo/VYXBCIvXwYyfISEVHrlFpW3Ca+nPKgIb9sP7vyjCf/pm\neGS4fdUNKKL/cC3M3Ai3dIGXRkBkkO21JgvM3gVvbIAB0fDGtRBrZ+3mDHh6s7Iz+KgfdLdxLqG3\nwAfHYfpxeKIZPNsSPKpE7AYrvJ8BH2XBcxHwVFh1i4T9BmFcHvg5wswQaFolV59ktRDh4IjbFbwB\n1Kt0LkEcPy7y+usirVqJREaKTJoksnXruRfi1OPcoNOJbNmi7IaHDhXx9VUdox59VHWPKrCh7jgX\n6PUiv60SuesREb8YkYE3KXtizTn6sCeliTw3XRVKDRqnGo/URfFjMovMXyfSaYJIy/tFZq8U0dvR\nsp9GnlbkhYUigY+LPDxXJKUG10uLRWTePpHY90Wu/VpkTw2drxIKRW5erjpQLThu389+WYZI7HKR\nUZtFkuzo+NcXibTYKzLyiEiKjSYoZRarPJdvlZBkq3yjtVbrHmayWuUjY5lEluXLX+bzkE5dRqBe\npXPpQgQOHVKl9kuXQk6OSh0MGaI8VcLsqBvqUTusVkhIgN27VZpmxw6VomnZEvr1U6NvXwiuRc1S\nG7QlsHodLF2jIvq2LeH2UXDLDdCwlki8Msp1sHg9zP0N9h2De29QEX0LG94xVVGgVYewny+FyAYw\n+VYYXku6KE0DH61VOfpbu6gcfVQN/ji/HYVX/gAPF3h7CFwTa3ttbjm8uQvmH4f/dYSnOlaP1gEO\nFcHkA5BUptI3Q238rqcZ4NlTsE0LH0fDKBt3ESvLhSfyoasbfBQEoVWsOA5azTxpLMUbBz51Joik\nagAAIABJREFU9Sba8cIZ610KqE/pXEZITla54zVrVJohKEiR0ukRG3vlN2U+H+h0cOQIHDwI+/ap\nsX+/IvPOnaF7d9XYu0uXuhUu1YbkU4rcl66G7buhT3cYOVSNukopQW1KW/fBt0vh13XQvZ2yJh41\nUB3I1oZ9ifDZb/DrFhjZEx6/Ebq2qPk5RzLgvdWwdD/c1xueHgKN7eT0rVZYegxeX69I/7XBcIOd\ncwytAT7YB58dhLtbwEtdoYFn9XXZOnj5ECzJgJdaw4RYcK3CwToLfJAJ07Pg0VB4PgK8qqw5ZRKe\nKoBDRvg0GIZWOeMpE+EtUznzzXpedfXiXie3q6JgsZ7wL1NYrXD4MGzefGbo9Yq0To9OnaBx46tn\nEygvhxMn4NgxNQ4dUlF7aqrKvbdrBx07qs+lQwcIrOFw8lxgNMK2XbDidzUKCmHYQBgxRNkQ+3if\n2+sdS4bvl8G8leDtAffcAPeMqD03D6A3wi+bYMZySM+DCTfAuGEQYsM//jRE4M8TMG017EyGJwbB\no9dAoJ3rtlph8RFF9M6O8PJAGNnK9u+ZzgxfHIT39sCQSHi9B0T7VV9XZlYSy49PwH3RiuwDqlgr\ni8CiAph8Cjp5wbQmEF3lDMUgwgdF8GExTPSDyX7gXsWtdaXZwGRTGT0dXXjb1YsQh6unNqWe8K8g\nZGbCnj0qTbFrF+zdq6LbNm2gbVs1mjeHpk0hKkrJCC8niEBhoSLwpCRlTXB6JCSolFfTpiot07Il\ntG6tSL55c6Ua+jeRmARrNqixaRs0j1UHrsOvhc7tz/2gPSNHKWzmr4TMPLhrGNw9Atq3qNuGfTIT\nvlwO3/4OHWMV0Y/oAc41ZCjMFvh1D0xbA0Xl8L/r4N5e4GHns7JYlQXC1I1KLvnKIBhu5/pMFvj6\nCLy5E7qFwhs9oI2NlIvFCnNT4JVD0CcYpsYpuWVV7C+DicnK3fKjaBhoY9NYXS48WQCtXWB6EERX\nOZRNt1p41lTGEauZj1y9GeB09htNx0RDnHHhyo2Q6gn/CkdBgboTOHRIjYQESExUm0OjRhATo+bT\nIyICGjRQ6aKgIPDzu/B3CDodaDSKzAsKFHFnZ6uRlaWuNS1NEb2zs7priYlRKazYWEXysbHQpMn5\nad/rgpxc2LAV1v0J6zara77uGhXBX9sfgu2oUGpCfqFK1SxYBQeOq1TNncNgYLe6FVcZjLB0u2o4\nsu8k3DdEqW2a1tIBq7gcvtkCn/wB4f4weSiM7GB/kzJZYN5+eHsTBHsqeeXQ5rZ/L8xWmHccXt8B\nsX4wtRd0tdHFSgRWZcFzB1Uk/3576G7jM8wxwpRUWFYIrzWGcQ2hao1gikl4pgAOGuGTYLi+SvrG\nJMKXZj3TTOU84uzOMy6euFe6eDPCN2iYgYbZNKIzdZRJXYaoJ/yrFEYjpKSoc4H0dDUyMhSx5ucr\n4i0oUGkSf3/w8QFvb5Xj9vZW0sHTensXFzUcHNQf8mlYLGAwqGE0qrmsTElPTw+tVqUIgoJUiiUg\nQG04YWFqhIZCeDhERiqir2uXp38CETiZDFt2wNadas7Ohb49YFBfJaFsayeFURtSs2DJenUAu/co\nXNcL7roehvauW15eREkp56xRRVJtmyj9/E197HeXOo0jGfD5etVlakgbePpa6G7ncBWgxKDkldO3\nQrMgRfQDYuxH9D8ch6m7IMILXusBA+wUi23MhSnxoDHC23Ew0oaevrQiT/9JFtwXAv/XGPyrbOZa\nq/B2EczSwtN+qlK2avpmo8XIZGMZ4Q6OTHP1plmVQ9ldlPN/5BCME1MJJYp/+VbwEkM94V+CKCxS\nreguBZhMKvKuTNIlJeq8wGSiQnOvHp/G6T9eR0elu3dzUxuDm9uZDeP08PVVm8d/ec5QWgq7D8CO\nPbBjryJ5Vxfo3U2NPt0hrk3dou6qEFHR+9KNaqRkwg394aaBqkDKo446/sx8RfDf/Q7FZSqaHzsE\nYmpRapnMsGQfzNgAR7Pg4f7wSH8Ir8EXJ70YPtkGX++GwU1hUl/oaoe8DWaYexTe2aMi+v/rqoqn\nbOGvfJhyCFLK4NU2cGdkdb8dkxW+yoE30mGQH7wRWT1PbxbhmxJ4pRCGesCbgRBRRX1zymrhRVMZ\nB61m3nLxYoST61mHsvmYeYc8tlDGFBowHB8cruBUzmnUE/4lBp0OGrWHRuEqmhzUF/r1OveDv3rY\nhk4HB4/AngOqqnXXfkhMhrjW0L0TdO+sSL6uVga2oDfApt2wbJMieRdnGDlAjb6d6p52KtXBkq3w\nwzrYcQxG91FGZn3b1X5GkKaBrzbB7D+heShMuAZu6gSuNXzv/Znw4VZYfgzu7QgTe0G0nYPtMhN8\ndQim7YW4YKW6sWVZDLBbo3L08cXwf63VoWzVoiirwMIClb6Jdod3IqGjjd/5NeXCpAIIcoIPg6CT\nW3X1zXRTObPMeh538eAJZw88KhG9BWEeRXxMPjfhy1ME482VLcWsjHrCvwRhNsOufWfyxbv2Qavm\n0KurIqNe3dSGUI+akZOryP3A4TNzQhK0iFUHq53bq9Z/7dv880PdU5mwcrMam/ZA++YwvJ8i+VZ2\n0iC2YDIrm4P562HlTujTFu4aCKN6gWctdwMWK6w6CDM3wdZEGNMDxg+ANjXk9K1WWHEcPtwCCQXw\neE94pBsE2EljFxmU6ubj/dA3HF7sCp3sqIf2Fyqi310IL7aCcTHgVoVbReD3YnjhFDgCb0fBYBt3\nt/FGYXIBJJnhvUC40ZOzInYRYaHFyMsV6pvXXTxpVCV9swcdL5ONN468TigtOJNDE4TNaGiPL35c\nZmqGc0A94V8G0OlURLp1p5L/bd2p8r2d2yuyOj2io84v7XA5w2SClFQVpR9PhGOJcCwBjpxQG2dc\na/XZxLWG9m1V4dP52iFURpEWNu6GdTvgj78gvwiG9Ybr+8KQXhBoQ0Vi9z2YYf0+WLQFFm+F5hHK\nqfLWfjXLKU8jKRe+2wZfb1a+No/0h9u6gVcNZwLFevhuL3y6Hfzc4enecGs7cLHz+5NeAp8cUMqb\n66PghS7Q2s5B9R4NTD2iGpE83woejrFdXLVNqyL6DCNMjYSbg6pvjOlm4dVCWFYOU/xhvC+4VFm0\ny2LiRVMZehHedfWml9PZhJ2LmffIYzNlvEgII/E9K32Tjo7pnCQNHW/Tmliu3Ma29YR/GUIEklJU\nSuLgkTPRa04exDZREWyLpkoqGB0JTSIhIuzCKVguJEwmyMqBU2lwKh1S09WcdApOpkBGlipmim0C\nLZtCy2ZqtG4BYQ3/vbOBIi1s2adSNZv2wNEk6NkeBnWHwT2gY8tzk2LqDPD7HlUUtewvaN4Ibu4L\nt/SFJnUoztLq4Jdd8O02OJoJd3SHcX2hfWTNz9uXCTN2KHnlkGbweA/o08T+57Q/Dz7YCytSYGwr\n5WIZZefg/M9ceOsoHCqG/7WAR2KrNw0H2F4Cr6bBsXJ1GHtfA6jaiz7fIrxTBHNK4CEfeN4f/KvI\nc5KsFl41lfGX1cwUF0/GOLnhVOmN6LEyGw2z0XA7/jxOED6V0jc6LMwllV/JYgyNuItGuHJla/Lr\nCf8KQnm5SlkcS4DjJ9XjlFRISYPcfEX6EaGKCMMr5tAGEBQIQQFqDvQHf78Ltzno9VBUrAi0qBg0\nhZBXAPkayMtXj7Ny1MjMUQfYDYJVTj2qYkQ2gpgoRfJRjf99jT1AZi5s3a8qXTfvhROnoFtb6N9F\njR5x4HaO37dACyt2qLz8un3QqRnc1Fvl5huF1P58swV+Pww//AUrDsA1LWFsb7g+rubcvM4EP8fD\nlzsgQ6tSNg92gVA73vgWKyxPhun7IbEInmgPj7QDfxt3DKfllW8fhSw9PN8S7mlSPXUD8FcF0R8t\nh5caKaJ3rcKvWqvwYRF8qoU7vOElfwivshvki5X3TOX8ZDbwuIsHjzp74FU5vYOwjBLeJZc4PHiB\nECIrqW8E4Xfy+Ixk2uPL48TQkDpIpK4A1BP+VQKjUUXHGVmQlVtBqNlKbligUdWhmkI1F2uVzNLH\nG7y91HCrkGC6uSoFi5OTigpP/505OKho3GQ+MxsMUFZ+9nBwUBuKvy/4+UKAH4QEQ0hQxQiu2JAq\nNqWQ4AufpjKZ4GAC7DgI2w8qki8uhd4doHdH6NMRurat3VPeFo6nqQh+2XallR/UUeXjR/SAoDpI\nTEVgdwr8sF01GYkJUbn5O7pBcC3NTA7nwMydSkPfvbEi+uEt7BdjlRjh26Pw0X4IcIOnO8KtTW2n\necxW+CkV3j0Gjg7wXEu4tXH1JiSgUjevpyuif7ER3G+D6MutwhdaeL8YrvOAVwMgxqX6gewXZh2f\nmXTc6uzGcy6e1apk96LjDXIwIvwfDenB2f4NJyjlAxIpx8IzNKUjZ3JvglzxSp16wq9HNYioSLyk\nVDXhKC1TRT5GIxhNisgtFpBK60WUGsXFRRGji4vaHLy8wNMDvDzV7Ob230owLRZlJbzniBq7Dikz\nsugIFbV3b6dIvkWT87OlNhjhz3hYtQuW/wVlerihhyL4QR3Bo46B5NFMWLBDkbxV4O4eMKYnNLNR\nxFQZZUaVrpm9G5I0KpIf1wWiapBhnixSHjffHYNrIpShWe8w2z+ncjPMSVbdpqI8VY7+ulDbazdr\n4bU0SNTDixG2I3qDCLO18FYR9HCD1wKhbRU7bLMI31kMvGMqp6ejM//n4kXTKgeyaRh5jzx2oWMS\nIYzGF8dK5F2EiZmksIF8HqEJIwnFqdL/J1PMTA5wL21ozXlU0V0mqCf8SxDf/gZxzaFt08vP/uBS\nQqEW4k9AfCLEJ6hx8AQE+0OXNhWjtYrefc9T9mq1wqEUlaJZuwe2HlbFUMO6KkfKjk3rtsGJwJFM\nWLRH5eY1ZXB7N9VkpEuTml9DBLakwNy98Oth6B0F47qqaN7eIazZqnrGzoiH3TnwYBt4NA4i7dw1\nZJTDZ4kwOwl6B6uIvqcN90wRWFkI72ZChkFF9PeGVJdh6q3CnFJ4uxDausIbgdC5isTSKsIii5Gp\npjIiHJx43cWTzlUOZDWY+YICFlLM/QTyEIF4VsrDG7DyExn8QBrX0YCHiMK3kgqnGAM/cJTNpHM3\nrRhGzFkbwZWGesK/xGAwwsOvwa7DSuoX11wRUvvm6nGbWBUp10NBROXbT5xSB6lHk8/M2lL1ecU1\nh3bN1GjfAgL+QbWuCCRmwPr9amw4AH6eMLAjXNdZzf513DxEYFcyLN6rPG10JqWVv7UL9Gpa+x3G\niXz4fp9qHejpAvd3hjHtIayG95deopQ2sw9DI28Y3w5ua2ZbRQOwqwA+OgGrsuHuKHiyGTS1sSmY\nrPBjPryXCU6oJiS3Blc/jC23Cl+VwPtF0N4VXg6A7u7ViX6ZxchUUzneDg687OJZzfemDCtfo2EO\nhYzAhycIpgFn3oQVYS25zCCFFnjzGNFEVUrvmLGynCR+4jj9iGAMrfC9CvL49YR/CaOkTJXf7z6s\nItODCcpJsXGoIrIWTdRoHqXmIP8r0xlTp4dTWZCSAckV42SaSs2cTAMfL2gWqfTuLaOhVbR6HBn2\nz7uFiag8/KaDsPGAmh0cYGAHNQZ1Uh7zdYXBBBuPw2/7lAWxlyvc3AVGd4LOTWr/+eWWqgPY7/fB\nqSK4sz3c0wE62rAnOA2zFdacglmHYHMm3NlcHcLG2fG3N1pgUTp8kgBZOtVl6sEY8LdxSF1iga9z\nYHomxLoroh9i4/ew1CrM0CoXyx5uMCWgekQvIqy0GHnLVI6TgwMvuXgyxNHlLL29EWEBRXxGPr3w\n4hmCq9kh7KaIT0nCEQeeJKZann4n2cwmnlA8eYg4IrkIfh2XCOoJ/zKDyaSi2SNJcCIFjqeor4+n\nKHVFk/CKEQGRoRAWAuEVIyxEkeOlsinoDcpALLsAcgogO1/NGbmQlg3pOWoUlyryjo448/5iGyuS\nbxp5/ukYWzCaYE+CSs1sOaRmL3foH3dmxNjJb9tDfgmsiodl+2HtYVUINbID3NgRWtahiU2JAX47\nAvMOwPZUlaq5uwNc27RmN8wULXxzBL6piOYfagt3NAcvO2nCHD3MOgkzEqGlr4rmbwivbn8AkGVU\nPjdf5Sjnysnh0NVG5K+xCJ9q4bNiGOihVDdxNoh+tdXE26ZyjCK85OJZzQrBgrAYLR+RT1NcmUwI\nbTi7oCKRMj4jiVR0jKcJgwk5K4+fTDFfcZAC9DxEO7pwRv9qRdjCCdrTGL8qB71XEuoJ/wpCkbYi\nEs5U0fCpLMjKU3a7Wfkq9WEyqzuBID8IDoBAX7UJ+HiBjyd4eyp/F7eKQ9fTw9FBRcuOjuqxVdQB\nqMWqZrNFEbjeqGadAcr1Kq1SUgbaMvVYo4WCIigoVs8LDoDQIGgYBKHBam7U8OwREnBh+vqKQFIW\n7DwGu07AX0fhQJIqfOrTFnq3UaPxOUTwoPL6+1JhdTysjIdDGTCoFQyPgxHtoWEdirLKjLDyOCw8\nBKtPQL9ouKu98p33qkEOWm6CJUlKbbMnF8a0gHFtoF0N3aq25CuSX5WllDZPNIN2dgq+DpbBx1mw\nWANjguHpcIixUciWZRY+KobZJTDSU+noW7jaJvp3TeXoRHjRxZMbnFxxrET0VoTVlPAh+QTgxGRC\n6FaFkLPRM4tTbEPD/UQymjBcKuXxC9DxA0fZQRZ30pLricap0v8fJ4t5/IUzjjxEf8K4RIysLgDq\nCf8qg05/hnBPzyVlapSWQ0m5ImyDUaUfDEY1RBTJW62K5B0dlFzSyVFp9p0cVfWvu6tSori7KSsA\nHy/w81ZRuI+nqkAN8lez10U0TTNb4ES66gK1N0FJJPclqgYj3VqoTlDdW0KX5uo6zxWpBUojv/Yw\nrDsKIT5wXRsYFgcDWqgNtDYU62HFMVh0GP5IhB6RcHMbGN0Ggmso/rQKbEpXKpslSdAjFO5tCTfF\nKt96W9AY4PtTMPOk+tk+Eqs8bmylbcwCSzUqok/Uw4RQGN8Qgmy8p8NG1YBkcTnc7a0cLKOqyCst\nIvxmMfKBqRwr8KyLJzfaIPo1lPAxBbjgwDMEMwCvs2STBRiZQypryGU0YdxDY7wr5fFLMbKQE6wi\nhSFEcTst8K6U/smmmJ/YSQr53EpXehJbL8u09Zz/mmzrCb8e9iCiOj0dOaXUMweTIT4ZjqVBo2Cl\nmunYVDUJ6dgUGtQgV6wJuVrYcAzWH1WjWAeDW8O1rWFwG/ttAasiUwtLj6oOUttToX+0IvmRrSCw\nlo3nYD78cAwWnIBAd0Xyd7WAMDubg4iyJv4qCVZmwfAweDgW+oXY3njzTCo/PyMbGrvBk2FwU2B1\nxY2IsFEP04pgrxEe84UJvhBUpTLWKMICi4HppnICHRyZ5OzBUDsR/ScU4IoDEwlmYBWiL8bE96Tx\nG9lcT0PG0pjASkRuxMJykviFE3QnlLtpRXClu4IS9CxhL9tJZBhxXEdbXLkMy9DPA/WEf4lBBF76\nBlo0hnbR0Dqqdp/zqxF6o1LLnEiHExnqYPVIKhxNVTn31pHQpgm0j4G4GPW11z9QN2UXw5/HYdNx\n2HQC0jXQvwUMbKVGm/C6pZ1E4FAOLDumiP54HlzfAm5qrZqKeNciFEnRwo8nVJMRrRHuag5jWkLb\nGqTjmTr4LgW+SVIVsA/FKMVNoJ3vtbMEPs9WUf1NQfB4KHSycU5iFOGnUpheDHqB//nBGO/qnvSl\nInxr1vOpWUcLBycmuXjQp8phrAVhFSV8SgHuOPCUjYi+BDMLSGchmQwkhPuJPKtC1oKVdaQyj6PE\n4s9Y2hBV6UDWiJk1HGIVB+lBLKPohG+lZieZ5BJMAK715mlnP+e/JtsrmfCNJvhwERxMUpFpYiZE\nNYQWjdQm0DxC+a40i4CGFyi3fSnAYoEsDaTmwqkclWtPyq6YsyCnUHnOtGikPo/mjRSpt4pU5xL/\nBCKQkANbEmBrgprzSqFPM+jfHPq1gI6RNR+YVobeBH+mqHTN0mPq325oqaL4fk1qtkUAyCqDXxJU\nJJ9YBKObqtx8n3CVWrMFowWWZymS35qvcvMPRKuuUjYLqizwUz7MyIF8k0rbPNDAdtpGYxFmauEz\nLbR2hWf8VHWsY5UXzhcrs0w6Zpn19HFy4Wlnj2o6ejPCMrR8RgG+OPKkDaIvw8zPZPIjGfQmkAeJ\nJKISUQvCNjL5jiP44cb9tKFVpeIpK1a2kchCdhNDCLfS9aw8fTElrGIzRzjJQ9xK40qHuVca6gn/\nEofRpKLY4+kVc5qKaBMz1UFo4xAlC2wcAuFBEBYEoQFqbuCvyvcDvC+NjcFigcJSyC+GfK2ac4sg\nW6PIPbsQsgogo0AReojfmfcXE3ZmRIeqTbCuhFsb8kuUHn5Xipr/Oqn6uvZpBr2bqrldo7p/hiLK\nanjNCViToMi+XUMY3lIRfds6mLqllsDik/BrIhwsgJHRSk45qLH9YioR2FEAP5yCn9OU0ubBaLil\nMXjZ2VQOlimlzfx86OGtiH5YQPU2ggD7DMLnWlhUBqM8VZepqoobgESrhRlmHT+bDdzo5MpEF89q\nnab0WPkVLTMpoAHOTCSY3nieRfSlmFlYQfRd8WccUWdp6QVhF9nM4ygWhPtoQ2ca/v0agrCPVBax\nGzecuYPuNK9E5noMbGAnW9hDD9ozmJ54YOME+gpCPeFfxijXQ1qeioJTcxVpZhUo4szWQE6RMuwq\nKQc/L0X+fl7g66kOJn091aGlh6tKG50eLhWHsJWHoA5sTx/cmi1gNKuDXaNJzWX6s0eJDopK1Sgu\nU//m762uI9gXgv0UqZ/epEID1dwoBMICz8+7pjbkaWFvKuw9BftOKZ+agjJVzdq1CXSNhh6xymb4\nXJBbCutOqsPW3xPV5zSkGQxtprpG1ZaPF4GjGnXouvgkJGthZAyMjoXBje0fvgIc18L8VJh3ShH1\nPVFwVxTE2JGrFptVNP91LmQaVST/QAOIssF1BhEWlsLnWkgzK3vicT7QsEpFlYiw2WriM7OeXRYT\n9zm784iLB6FVvG6KsfADRcxFQ1vcmUBQNdVNMSZ+JINFZNKTQO4jkugqRL+bHOZxFAMWxtCKXoSf\nJcE8Qia/sAsjZm6hCx2I/HsjMGNhG/v4g+20oAnD6EcgdZBOXQGoJ/yrAGYLFJYo8teWq1FSMZfq\nKqSURpV60BmUdNNiPXv8LcusMExzdqqQbrqolISbi8qde7mrXLmXO/h4KIL381Kzj8fFu9MwW1Ra\n5kAaHEyHg2nqcYkeOkWdPZo3PPfrKtTBn8mw/iRsSIbUInXgem1TGBwLLewchFaGxQrbs+G3JFhy\nEgwWuLGC5PtG2DYiO430cmVeNj9V5ehva6xcKjsH2P6+IvCnVpH8Ug0M9oMHGsJ1/raj+WSTStvM\nKYV2ruog9gZPcK7y4noRFloMfGHSYQQedfHgDic3PKusy8LENxTyM0UMwpuHCaRllWi6ACPzSWcp\n2VxDMPfSmEZVUjd7yWUeRynHxBha0ZuIs4g+kRwWspt8ShlNZ3oQ+/f/WxH2cYRVbKYBgQynPxGc\nMScqJB8f/HG+gg9w6wm/Hpc1DCZIzIXj2cqL5nAGHM5UZB8RAO0bQ1yjM3N0HYjYFvLLYMspRfKb\nkpWtQa8ouCZGjc7hdUsxaQ2wNhWWJSsvm3BvGBWjiL5jLdeWo4dFafBTmmoXODoC7oyCASG2i6MA\nUvTwXR58mwvujvBgQ7gnBEJs3D1ZRFhVDjO0sMMA93iriL6qfh4gW6zMNumYY9YT5+jMBBcPBju6\nVMvjH0PPLDSso5TR+DGOQCKqHIpmoed70vidPIbQgHtoRGilzUAQ9lRE9DrM3ElL+tDoLM+bFPJZ\nxG7S0DCKTvShOc4VWntBOEYyK9iIE07cwACaEvX3c8spZStrOcJebuNhwqilqcBljHrCvwSx5QQ0\nCYZw/0sj9/5fo9wAKfmQlHdmnMhRJJ9RCJFB0CJUKWXaRKjRMhQ8z9MaRQQSC5RMcluqMiZLLYZe\nkSqK7xcNXSNqP2w9/VpHNMraYNUp2JGter+OaAIjou03EzmNXD0syVDR/J5CJaW8LRKGhtr2nAfQ\nmlVh1Hd5cKAM7ghWTpWd7VRZp5qFuSUwWwuhzkpSebsXeDpWT9vstJqZbdaz2mLkFmc3xju708Lx\n7A9CELZSzldoOIqBsQRwN/74Vekdm0QZP5DOZgoYRRh3EEFQFd/6XWSzgGPoMHMXrehTJaJPQ8MS\n9nKCbG6gA9fQCpdK3yeJdFayiRLKuZ6+xNHi79SOEQO7+ZNdbKI1nejNEDy5sptH1xP+JQaTGQZN\nUxFqsQ5iQyC2ATQJgqhgiAyEqCBoFKiKe+xFdpcLSvWQWXT2SNOoQqY0DaRqVHenJsEQHawi9JgQ\nZRPcIlQ9rgvx1oS8UtiVAbvS1fgrTVWz9mgMPSOV+2THsLofEueWw/p0FcmvPaVSM9dFwdAouLYx\neNcis00qhcXpiujjixW53xYJw0Ltm5wZrLCqUB2+rimC/r4qkh8ZCG42fkf0VmFpOXxdArsNqtnI\nQz7QwcYhbIlY+cVsYLZZTznCA87u3OPsTkCV/Hw5VhZTzFwKccSBBwhgFL64VapqVWmZYuaRzhFK\nuI1wbiH8LAdLC1a2kMHPnADgdlpUI/pTFPAbe0kgh2HEMYhWuFV6jVSyWMWf5KJhCL3pQtu/q2vN\nmDnAdrbzB42Ipj/DCaAOHWiuANQT/iWMUr1KVyTmKgI8VXBmTi+EonJF+mF+EOavHgd5Q3DFCPQC\nXw/w8zgze7mpQ9p/a6MQqcj9G1V+XKuvmHVqw9KUgaa0Yi6DvBLILamYteowONz/zAjzUxF740C1\nuUUGQQOff+9OJ68U9maeGbszVD6+SwR0baQi9x6REH4O0s4SI2zJhD/S1Dilhf4RMDgSrouEZrWY\n2llF9YFdmgm/ZajUzY0RcFMjGNjAfiRvFlhfrA5gl2ggzhPuCoGbAyHQRspGRNhtgLnM47IyAAAg\nAElEQVSl8FOpcqu83wdu9gIPG/rOg1Yzc8x6FpkN9HFyYZyzOwNspG3SMPIDRfxMMV3w4H4C6FlF\ncWNGWE8e80hHh4W7aMRQGuBeKRo3YmEdqSzkBAG4cxvN6UroWa+TRB6/sY9k8rieOK6hFW6Vcu5p\nZLOazWSSy2B60Z04nCu+hxULh9jDFlYTTCj9GEYojf9+bj4p+BOG8xXsmllP+JcxjGbI0UJWEWQV\nK3lhfikUlJ6ZtZXIt7gcyo3KhtfVSRG/h4tS5Tg7Krmfs1N1bbcImCxnD4NZkbzBfOa1fD3Ax10N\nX3f1dZA3BHiqzSfAS5F3A98zs9cFaohitqi0zIFsOJAFB7PV41IDdAqHThEVczg0Czq3DaXcBFuz\nYEO6GvEF0KWBUtMMagxdG9Z84Aqqkcj6XFiWAcsywc8F/p+9+4yS67zORP1UVYfqHNCN0Mg5RwIk\nmCBmihQlUhpFS5Yseyzn8TiMJ9wfXnNn1pp7Z5xmrJEsj4MkXwUrUxTFHMAMIhE5xwa60UDnVLnO\n/XEOGt2NBoM8GlEw9lp7fQesqlOnq4rvt8+79373B6bzgRY2TrryhlwIwsEi/9jJd7uYm+RjTXx0\nEjOugFNt+cDXBvnKAKmAX6rh09WXSx4QTpX6TiHjy/m09qDoMyVJn06Umz6urPIibfMVPbYa9i/U\n+YyGMaMECUsrf6Ddt7SZptynzHSzxjHR+pCcHzvuYcfMU+ejFlthrPjPYec8bKezetxvldssGdMd\ne8Y5j3vJGR3utNFGq5VGjweKDtrlJY+rUO093memeSOv7XPONt9xzmH3+n1N5kz8QV4Fdg3w/xla\nEFwC7FQ2BPB88RKYT/TRlibGelkJlWUkS3+2eYZcIZzsdPAC+86HY/32nQ+Tqi01rJ7GqqmX1rlX\nqGJ5M+vN8HIbL7TxwtkQ4Nc2c/sMbpvOjdOuTLWMtlNDPNrGo+28eIHrGkNO/gPTWfQm4woLAS/1\n860uvtfFlNKQl/9o08TCZYS68z8Y5qsDvJ7hQ1UhyN+aNKbD9aLtLOZ9JZ/2vXzGxkSpXy5Jujte\nOmYoOAwo+L5+X9GjRMxnItqmctzw7zYp/6jNj3W4UYNPmGGpsX9kt5SHHfO4k9ab4sMWmTtOyviA\nNg/bqdOgB6xxi4VjOPpW5zzpZae1u9NGN1ozCugDR+3zgsckJGxyv7mjOPxhvXb4geNet9J7rXCv\n0qs4uuddBvixWOyP8as4H/2n/xAEweMTPO8a4P8zsmyek70hsB/v5lg3RzpDUD/Zy/RaFjeFDU3L\np7B8Mksnv7mq5JWsGHCwm9fOXfIT/dwwlU0tbJrO9VPCgSNvZYM5Nl/gyXM81cGFTMjDP9DCPVMn\nFiq7aOliSNc83B36tDI+Min0hVeQiMgGgadTfHOQR4ZD3flP1/Bg5eUJWMJO2G/nM/6/fFqfwKdL\nkj45QTQPe6V9Ta8f63eTKp/R4AYVY+iWsD6+17e12anPB0z1US2mjCu/PKHPDxz1qja3m+lDFpri\nkgBQUdF2pzxql5ScB6x2owUjVTdw0llPecVZHW53gxutGZFECASOO+AlT8jLudV9Floxcq0p/Xb7\nsUM2W2STNR6Q9CY77lVk70bAHwiC4M/e4nlXLeAHAX/2UghisxuYU8+Ud0mn7E/DikXOD3G2P/K+\nsCLmVE844ON0HxeGmFHLvMZLvnASi5qY3xjeZfwkFgScGeT1DrZGvv08TRWh4uTGqWH0vmrSlbtb\nR1uuyOtdIVXzTEdYVbO+kXumcPdU1jVcWQoBunI81hsC/FO9rKriwQYebGTBFUA+HwQ2p0NO/ntD\nLCkNE7AfrmLq+HFTwk3h8ULW1wsZLxVy3pso86mScpsm4OYHFfzQgG/o1S3v4+p9VJ0p48oqB+U9\n5rzvOCsh5sNavNcUlaMi8aLANuf8wFGnDXi/ee4zd8yUqay8lx3xY7tVS3qfVdaZM0L/hBH7KU95\nVaced9joBqsui+hf9qS8nFvca7FVYtFGkTZoj8cc8Kz5Nlrt/ao1RtdXcNozprpe8po88hj7aXcl\nXN36pG9hhSLnBtnSGkavp3royzC1OkwkttQwrYapNTRXhd5UGa4NFdRXUP4z6hsJAtL5UOa3N0VP\nmq7hsIa9azj0jsHw7+sY5NxACPb1yXCDu+iz6kNBsdn14abXUvNPl1EoBqHw2I7z7LhwaY0JOffr\np/CH60IuvvltyiPni7zRGypQPnc+1JWfX8UdU/i3S7m1ieo32YyCgIMpHunhkW52D4fDRB5s5Avz\nJq6VJ6yXfyHNtwb53jCzSvhIFdunT8zLB0FgWzHvm4WM7+YzlsYTPlGS9Ndl1WrHVdqEVTRp/6jX\n4wbcpNLva7JJ1WWzXo8a8j1tnnLBevX+nYXWqBsT9afkPe2UHzomKeEhC20yY4xe/YC0Z+z3jP3m\naPIrNlk8KllbFNjniKe9Ki3jDhutt1wi2lACRYft9bInBQI3u8diK0eAPmPIXk/Y52lzrfdB/0lN\nlCMIFJ3xogP+QVKTJsu5igH/J7GfdoT/GfRjG/4gCIK+CZ531Ub4E1kqF4Jj20Aop9vWH4LmhaHQ\nO6O1Nx16IhYCf215SGtUloZrVWnYol9WEiZayyI+Ph6LOmiNGm4S6d8XiiGwZfJhJ2gmH/pwLhzS\nMZi9tPalw+utT1KXDDegpiomVYab0qTK8G5lSnW4YV08/t+9QfVn2NcdygfvinxPJ7VlrJvMumau\nmxwet7yDCWC5Ijt6eOECmyOAn1HBbZNDv30yk96CAk4V2NzPoz3hsO9cwAMNvL+R2+vC5qgJ3zsI\nbE7xnSF+MMz0BB+tDoF+3gQgD8eLBd8qZHwzH34xHy9J+nii3JwJKJsued/X71t65QQ+pt6H1I2Z\nEwtZRc/p9F1t2qQ9ZJoHTdU8jvvuMOQRxz3llJWaPGiBFSaN2Qw69HvCHq84ar053mulGS7pShcU\n7HDAM15TKuEuN1ppkXgE5EVFh+zyiqfEJdzsHgstHwH6rGF7PGGfp8y21loPqhVOswkEznndfl8V\nV2q5z2i25poe/kSv+aeAbSwWe4pR/cwhzgT4v/AaOoMgCGKx2H/GtCAIfmWCcwR//Md/PPLv2267\nzW233fYTX9PVZBej7N5UCHxDESAPRQCdyYdKitnCpePAqAEnQTTcJB5uHBePkyUhMJcnwrWiNKwn\nry6LNpOyEOh/UnrlJ/k7O1Mc7uVQDwd72NsVAn1nimWN4ZSn1U0hJbOqiUnvUB65L8vW7hDYX7zA\n693Mq+LW5hDgNzUz+S20toKAw2me7A3r41/oZ00V99fzvgZWVF55w0kVA8+mQ6rm4SHmlYZUzb+o\nYv4VQP5cUPSDfMa3CxnHiwUfLin3sUS56+IllyVrcwIvGPJtvV427B7VPqL+Mm4eWqU8rN2PdJiv\nyoe1uFXjGF49EHjDBY84Zp8u95jtAfPG8POBwGEdnrDHQe1ut9TdlqsfpZWTkfWaXTbbapJ6d7rR\nYnNGrqmgYL/tXvW0ClVuco95low8njFkn6fs85SZVlvrQXUR5AQC5+2w3z8oyFjm06bZeNUC/fPP\nP+/5558f+fd//I//8d3D4Y95k1hsNh4JgmDVBI/9s4rw/7laoRhKA58c4FhfKA18rC/0I73hRrW4\nnkUNLG1g+aRQF35O7Ztz5RNZrsi+vhDgt3TxWhenhkPe/cZJIcjf3PTmidaLdi7Lc3081cfT0XXe\nXR/q1txTT8Ob3NGcLwQeHeaHQzybYnU5H6wMq2wmomvgQlD0w3zGdwtZu4t5702U+UhJuTvipUrH\ngXwgsEfa9/T7kX4zlfqoeg+oUTOuEzatYLMuD2t33LD7TPFB08wyducckPWM0x51XIm4B8xzp1mS\no+4Ocgq2OOZJ+6Rk3W25TRZLjsoH9Bnwkh1e9Yb5ZrnTRrNcGvqblbHLa7barEGTG91ttgVjkrF7\nPeGAZ820xjoPqovUMS8C/QFfkzNkiV8ww60jdwODjjjlb8z2y6otvvIX9HNu77ak7dQgCM5Fx7+H\nDUEQ/MIEz7uqAT+T/9nx8P+nLAjoydA2ROtAmDw9M0jrYNi4dGog/O+NyRDA59eN9YX1NP+EIxLz\nRQ72h/TMtp4Q5Hf3MqcqTLJunBT6irrLpztNZF25kKZ5ri+srGnPhZ2ud9aFQL8oeeXrDILAG1ke\nHeZHwxzMcU9FOAf2vsrLp0ZdtI4I5H9QyNpVzLsrUepDiXJ3J8pUTPBmrbIe1u97+hUEHlLrIXXm\njqubD3VnBj3inKdcsEyND5hqk0ljePdA4JAeP3bcq9qtN8UD5lk2jrbpNuRZB2x20EyN7rHCKjPH\n1OGf1eF5W+131DrLvMcGTS7JlQ4btM2LdnrZLAvc4HYto7RwhnTb7TFHvGSeG6xy/zjqZquDviFv\nOAL6W8SizW3Icaf8jX5vmOEXTfNBiatYIvndBvhfxRoUcRK/FgRBxwTPu2oBP1+k5osh7z69iunV\nIc88pTIEuMkV4dpUQUM5DcmQm36nEe3/bssVQgDvydCdDteuFBfG+bnhyIfCv3FaJTNrmFEd+vRq\n5tSEID+r5s1lgd+ODebY28eu3tB39IRyBTMrw+h9XQMbGsO15m3SURdyITWzuY/n+zmZ4aaaMOF6\nZ11I2VwBp0F/MSyffGw49IoYD1TyQFVYJ192hd2htVjwSCHrh4WMfcWCexNlHkyUuesKIN8l71ED\nfqDfSVn3q/FBddZJXkZhdMt6wnk/0mFYwftN8T5TLiupHJbznFaPOSEl7z5z3W22ulEcfkjbnPOU\nffZpc6P57rJcy6hkaFHggGOe97pOPW5xnRutUTnq/XpcsNVm++20xGrXu13jKAmEPufs8qiTtlno\nFqvcryraKAKBdq856BuKcpb4hOluHgH6YSec8rd6bTPDJ7X4sIR3yPn9HNq7CvDf9gVcxYBPyKN3\npTg7xNnBMAo+nwo1Ws5HwNmZigA2HXZt1pZRUxaCVnXEr1eVhICZTITce7IkjFgTscij44scfuBS\nwjZXIFsMqY5sgVQ+9OFoHcyFkgID0ZorXtqAGspDb0wyOdqoLvrUynDm6pTKt9es9HYtX+TIYAju\nF313L2dTLKtldT2r6kNgX1P/9sE9CEJAf7E/9JcGQg35m2u4rS6M5NdVvfmdQDEI7M7yRATy2zPc\nmOS+Cu6vnFiN8qIdKuY9Ush6pJB1slhwf6LM+xNl7kyUKZ8A5PsVPGXQI/ptl3KHag+pdYsqpeNA\nPq/oZd1+pMMOvTaZ5H2mWqduTAR+MZp/3AmvaLNas/vMtcbkMc9Ly3nFUc/YL6fgLsvcapGKUXcR\naRmv2+NF2yWVu80GaywZqbiBNqds8azTjlnrJuvconrUqMIup7zhR9rst8ydlrt7pI4+UNTmFQd9\nEyzxC1psHKFuhp10yt/p9brpPq7FR5REOYacdiWaxK6NOBz7mp812F7tgP9OLV8Mu0EvgvBg7pJn\nCqGn86Sjjtp8MQT1QlSFExtVoROLNoOySGqhNB4eV5SEXhmtVaWXNpnasnBT+WlIJIy2IAibl44O\ncniAQwPh8I9DAxwfCitmVtRd8pV1YQfrW8kcjLahAtsGeW2ALdEa4NbaS76y8s0jeGjNB55J8XTk\ntXHurghB/vYKqq5wS5YPAq8V835cyHqskDUs8L4okr85XnqZHj1h9+uzBv3IgNcM26jSA2rdrfqy\nDtiQw+/3uPOe1WmWCg+Y6k5NqsZV5PTJeE6rJ52UUfBec9xltoZxUX+rbs854FXHLDHVnZZbrmXM\nXcQF3V6ywzZ7LTTHJuvNNX1U6WXBYXtts9mAPhu8xyo3KIvuHAKBNvvs9phurVZ6ryVuVxZF5UV5\nrZ532LeVqLTEx011/cj5hxx32pdHAf2HlUTKmDntunxRv4fN9FUVVr/5l/tzbNcA/5q9qyyVD5Ol\nJ4c4MXRpPToQAn1pnPnVIZAvHuWLat75HUOmGI742zoY+rYhjqVDEbKNNdxQHa5z3obeT3s+8Hw6\nTLQ+l6KvGAL73RXcVcHcKyRcCZOuzxSynihkPVPImR2Luy9R5r2JMmsnqK6BHgVPGfC4Aa9LuV6F\n+yOQHy9DTChF/ITznnBeubh7TXavyWNmwxJG/Vud87RTdut0g2nuMssqzWOi+Yyc1xz3vIO6Ddpk\nsfdYommUvHBB0X5HvWynszpcb5WbrR0zXSpt2C5bbPeiGnXW22SxVeIjgmd5x2yx22OKClZ5rwVu\nkoii8Ly0kx53xPdVm26xj4wprxxwwGlf1m/XBEDfpssX9HtEvY9p9KtKrnLVzGuAf83+j1gxoDdL\nezqc0HTRz6ZoHY48FVJEsyrDBOrcqmitZkF1CPQNP4FcAgwU2DPEjos+GJZLLkyyoZr11eG6sjK8\no3krO5MP6+I3p0M/X+A9Se6IIvjlpZcP9b5ohSCws5j3dDHniULW4WLBexKl7kmUuSdeqmWCOnk4\nJ+cpg54wYJe0m1W6T43bVaudAOTPSnnKBU86r1/e3Zrda7LFqi+TRDim1zNO2+yM6ardZbZbTVc5\nit4IBE7qtNkhWxy30BS3W2KVmSPSw9Bv0Ba7veINdardYp3Vlox0xEKnc7Z7yX47LLDMepvGDB7J\nGHLQ8/Z5Sq0pVrvfjDHNVH2O+aHjHtVkpUU+otGikdf32em0Lxty3EyfNNVDI8nYrFbdvqDfj9X7\neAT0Y8Xarla7BvjvMisUmfMjmsqZkrzkk8poHOX1ZdSWUlMSruXx/zOUSrbIYJ6BfFin3pe75N3Z\n0Lsy4dqZDQd4dKTD48oELRWRJy8dz6y85M3l/7QEdCHgeJq9w2Hn6q6h0M/lWFrBuupwEMi6qrAG\nvuJtdPAWg8DBHC+neSnNi2kGimxKsqkiBPqVZS4TGhtt7cWCZ4s5Txeyni3kTI3F3ZUoc3ei1E3x\n0gkTtaFUQNaTBj1pwElZd6h2j2rvmYCugQ5pz+j0tAvapN2hyd2arR7Hy0OnlOe0etZpaXl3muUO\ns7SMGwIyJOMVR212yLCMTRbbZJHGUc8LN43TXrbTISesstjN1pk5amh4UdEx+233ogvarXGjtW5S\nPSri79dhrycd9YqZ1ljp3jHqlUPaHfE9rTab7laLfEi16SPX0OMVp31FVqeZPm2K+8WjHELWSV3+\npwFPafBJDX5FSdToVdAq5U8l/aaSURvH1WbXAP9dZkEQRr0d6Ut+PkNXlu7MJVDtyYag258LJxwR\nAmrFKE8mKI2FNMhFj7u0MVz81i/y+flozRZC8a5MIaQ90oWQ2x7Kh2BclQiTnnXjvLEs7DS9uDlN\nKmdKtHE1lV9Z1/0nsVwxpF8OpTkwzIFUCPIHU0wuDcF8ZSWrq0KKZmEFE0jLTGgDxcDWDK+meTXD\na2nq4tySDP3mZKhZc6UInlBm+OVizrMRwJ8LijYlSt2dKHNXvHRCgTLCZqjtUp424GmDMgJ3qXav\nGjeovCzxCh0yntPpGRecNOw9JrlLs/XqxzRGEVbZvKzNc047qtdNWtxltmUmjdkQior2a/eiQ3Zp\ntcpMmyy2bNyw8CEp2+z1qjcQc7O11luuYhTPnzJkt9ft9LIKVa5zqyXWjMyODUsnD9njCeccssRt\nlrtL1aiu226HHPFdF+w2x70WeFAyejxQcMGzWn0FgZk+rdmdYtH5M47o8gVDNqv3ixp9ViKqGLoI\n9Bnfk/RZFf6VuElX/F5/3u0a4F8llikwXAhb91NRVU06qrLJFcMW/lwxpFaIKnOi1yZiIRherN4p\ni0eVPfGouiceVvxUlby9uvT/XZYucirDiTRH0hxNczQVHp/OhPrvi5MsrWRJRQjwyyqpeQcbS7oY\nVtBsy7A1E64n8uFwkBuT3Fgeri1vsVsMB4EtxZwXCjkvFnP2FvPWxEvcmShze7zU2njJFe8Azst7\n3qDNhrxkyEyl7lLjLtWWK5+wC/SUYc/rtFmXVim3aHSXya5XP6ZeHtLytjpnszPecN4qze4wywZT\nlY+jgs7q8bIjXnFUjaRbLXKjBWpGAXhR4IhTttjlgOOWme8ma8wzc+RawyTrKTu97Ii9FlhunVtM\nHxWt52Uc9Yp9nlaQt8I9FrplRKK4qKDdq476gZROCzxkjnuVRHmHgpRzfuSsbygzyUyf0ejmUY1Y\nO3X5opQdGnxWg1+UiKp9Co4Z9meyHpH0SxHQX/20zjXAv2Y/EwsC+gqcyXA6S2smBPHT2RDgT2To\nzDGznHnlLEiGUfqCJPMjn2h035vZUDGwK8vODDuy7MhwKMfiUtaXX/JVZS7rUB1vfUHRlmLey4Wc\nlyOAXxUvcWu81K2JUtfHS1Ve4RxZgR1SXjBks0Gtcm5R5TZV3qPqMjVKLgqIDXhBlxd0GZT3HpPc\npsk6dZdF8lkF23R40RnbdFikwSYz3KRFzbhmqz7DXnXMK47qNewmC9xi4RhdG+jW63V7bbVHhXI3\nWO06y8fUzqel7LfdTq/Ky1rjJittGDMrtk+HA55x2EumWGi5u023fNSs2UEnPeG4RyRNssBDWtw0\nksjN6nLWt53zfXXWmO6T6oQN+YHAkBd0+ytZp03yOXU+Kh5tEnn7DPsTOc9K+lUVfmMkog/yu0gs\nEotdvfX41wD/XWjZ4ttLHL7bLAgYKoZA3ZXnfI6OXCg10BEdt2U5mw3XkhjTy5hVHnlZCPBzysNJ\nTtPL3rr8ceLrCJzOszvLrsh3Z2nNs6yUdeWRl4Xc+0Tj/cbb2WLBa8W8V4s5rxVyjgYF18VL3Rwv\ncXOi1IY3AfhA4ISclwx5wZAths1RZpMqm1RZp2JCqiatYJteL+ryom61Stxqkk0mWa7mMk7+Isi/\n7KytzpmrziYz3GL6mMao8Nw5O5zyiiOOOm+d2W6y0DLTRsTJwnPm7HHYFru1OW+tpa63agw3HzY5\nnfaGVx2y21yLrbHRbAtHkqxFRWfstt/TLjhhkU2WukPtqKqYAa2OeUSr5021wXwPjknEDjnmjG/o\nslmzu83wCRXRiMJAXr9HdfsrFDX6NbXeP1JTn7NNyn+Ts12F35L0K+JRtB/kt5L6T+S3UfNjsZI1\nb/l7+Hm1a4D/LrNCQNVrIRg2lTKpJPT6EuoS1EVrbSLk0qviIXdfFQ+pl7JYGPmWRdRMXCSCZmyT\nVVF4XAgiuidKyOaCkEpJjfOBAoPROlCgv0BPnt7IewqhxEAiRlNJeO1NpUwtDSc0TSllShktZSGQ\nt5S9M+plIguCwJkCB7IcyLE3G/q+LDXxEMxXl4UR++ryMJJ/q8idUDN+TzHv9WLe68WcLcW84SCw\nMVFqY7zExoiimajx6aJ1ynvFsJcMedmQPG5RaZMqt6gy6Qoq450yXtbtRd2267VYtVs02qTpMg0b\nQrpmuw4vOWubDvPVucV0N5mucVy9fF7BHme86phdTltkqhstcJ3ZYwaAhxvUWVvtsdshs0xzvVVW\nWDim0iZlyD7b7bJFTtYaG610vapRw0RS+h2y2QHPSaqx3F3muUFJdJcRKOqw3VE/1OeYOd5rnvep\nuBh1C/TY4qyvG3JUi4+Y5kNKo0Rv0bBe39Ltfyk1wyS/rsptYmICgZznpfypguMq/K6kT4tFn2OQ\ne5X0/01hL8l/S/mvXNXRPdcA/11pQRCCalf+UrTcWwiTs32F0PvzDBfDiHqoEK7ZIpkgTLRmIwAv\niqSOo5VRUsjRcWks3CBKIy+PUzHOaxKXvDoRbjoN0UZUHx1PKnl7VS/v1HoKgaM5juSFay7UnDmY\npToeJlCXRtH6ilKWl9H4Nm8NikHgaFCws5i3I/I9xby5sYTrE6U2xEtcHy+xMJaYsB5+5BoVbDHs\ntcjPyrlBpVtUukWV+com5OLzAvv0e1WPV3U7K+0GDW7V6EaN6iagdwZkbXXOK9q84bxFGt2sxU1a\nLmuKKig6oN3rjtvmhGnq3WSBDeaqHbeBdOqxw37b7BUTd72VrrNc/SgADxSdctRuWxyz33zLrLLR\nbPNHovkw4j/ooOe02m2O9Za5Q/OoObJZA057xnE/klBhgQfNsEki2ggKUjo8ps23xcRN9wmT3TNS\ncZPToddX9fqGSjdo9DkV1kbvX5D1iJS/EBhU4feU+6iYUkEQkH+a1H+heJzkv6f8l8Ri5QRFxH76\n5W4/Q7sG+NfsZ279xZCCOZXndJ4TOY5H64l8WD20sJQFo3xJ5A3vgPPJB4FDQcGuYt7uYj5aCxpi\nMeviJdbGS6yLvCb25pxam5ythr0uZath7fKuU2GjSjeotFJSyRUkd9ukbdFjix7b9Jqm3EaNbtRg\nldrL+HhoN+g17bZod0Sv1ZrdqMUNpo6ZGkXYPHVQm9edsN1JzWpcb54N5moeN8pvwJCdDthhvy69\n1lhivRVmmTZOBO2Cvbbaa6ukKittsMJ6FaOkj4f1OexFh2yWUGKJ2yx0i/LoOWG0fthxj2r3mqnW\nm+d9Gi0blWht0+7bznlUnVVafEy99SOPp+3V7e8MelqthzT6rDJzo/MPSfualM+La1bhd5V5QExc\nEBTIfY/U/4N0GNGXfUIsVkqQp/+bdP0Xpv0NFTe+6Xf/82zXAP+a/dQsGwQ6CrTnOVcI/WyeswXO\n5MPjM4XwbmR2SeizSphbytwS5kXHk+ITD95+M+sOivYV8/YUC/YW8/YGBQeLedNjCavjCaviJdbE\nS6yKl2h6C3AvCByUsV3KdinbDEsJbFBhQwTwS5VfEeD75ezQZ6teW/QYlHeDBjdocL16TRMMzg4j\n825bnbNFuwFZ15tmo2lWax4jPUwoP7zPWVudsNMpk9VeEeRT0vY4bIcDTmmz3ALXWWaROWM0bdKG\nHfSGPbbq0Wm566ywwZSo7p2wkuaMvQ55XpsD5tpgsfeYbP4ISOeltNrshB/LGjTXfea4R3lEywSK\neryuzXf0222qB0zzYRVaoscLBj2l29/JOaPBL6r3iZHSyqLzUr4k7W+VulmF36NQSKIAACAASURB\nVFFqY/jaIE3mK6T/hFgTFf+e0gfEYnGKafq+TPd/pWQWTf+ByruvRfjjX/OzBturHfC/PBCojdMQ\npz5aa+IhfVHmnYPfP8UKQWA4oL841nuLdBfpKdJdCI8vFOgscCE6HioyOcHUBFNLwnV6guklzCgJ\nj2eU0PgTAPpF6w2KDhULDgUF+4t5B4oF+4OCoSCwLJ6wMl5iRSxhRbzEsnjiLSN36Jb3hrQdUnZK\n2S1tshLXqbBehXUqrkjRECZb9+i3Va+tep00bJVa69W7QYMFqi5LuBJq1+xw3uva7XDeZBU2mOp6\n0yzScNlr0nJ2a7XNSbu1mqHBBvOsN8ekcc1TGVn7HbPTfkectsAs6yyzzHzlo6p2CgqOO2CvbU46\nZI7FVlhvnqVjNoM+HQ57wREvqdJokU3m2ziibQO9jjvhMWds1mSFue4zxXUj1E/egA6PavMdcUkt\nPmKye0c6Ygv69Pm2Hl9RolmDX1bj3pFEbN5+KZ+X9SPlPqTCb0tYAIJiL5kvkv4flFxH8o8ouTX8\nnRUG6P0SPX9O+Rom/Qcqb37L38XVYNcA/11mhSDwLy+EQNpbvLQORE4I/pWxUFY3GQuTtckYpcJk\n78U14fIBwUXkRc1WQrokE5ARrUGYpB0KQs8G4XvVxkOvG7U2Rt6QCDel5kTk0XF9/M2bk96u5YPA\nqaDoWFBwtFhwNCiEIF/MG8KieMLiWMLSeMKyeIllsYQZsfjb2kRSivZL2zXiKV0KVktaq8JaFdZI\nanyTUc4ZRfv0267Xdn0OGrBAtfXqbNBgpVplE9A0RYGjemzTYZsOp/Rbpcn1ptlgiqZRU6AuWr+U\nN5y23UkHtFtgsvXmWGfOmKlRhBU2Bx33hoMOOG62FmsttcqiMY1RF2vm99nuoDc0arbCekuskRx1\nzpy0E7Y65AV92i1wk0U2aTTj0ncl5YwXnPC4tG5z3GuOe1SMqnEfdEib7+r0rAYbtfiIWqtGTaw6\nqsdX9Puhau/R4LOj+PlAzrNSPi9vjwqfk/TLIzX0QeE06b8g+2VKHyD5b8RKVkYX10nP/6D3i1Te\nyaR/RzKqyEmd4vR/Y+bvUrnwit/1z7tdA/yfM8sGgcEigxE4py9W1QQhkOdGrYVxH1Egaq4atZag\nPDbWK6MNpSraUH7adxRBELggcLpY0BoUnQwKTgZFJ4sFJ4OCs0HR5FjcwljCgnjC/FjC4gjkp79N\nYIc+Bful7ZMZWU/JWqjcasnIw+h9/MDu0dYvZ7d+u/R7Q5/DBs1T5Tp1rlNvtTqVE2jbQIdhO3XY\n6bxdLqhTbr0p1ptqhUlKx70uEDijxxtO2+mUs3qsMMN15lhtpqrLyi0zDjhut0MOOmGmqdZEIF89\nCrwDgQvaHbDTATvFxS233jLrNIwC56KiNvsd8ZLT3jDVIovcapa1EqM6ZbsdcNKT2ryiyQpz3GuK\n9SO18wUpFzyt3fdldZrmg6b6gLKRapy8QU/r8Q8yDqn3C+p9UunIaMJBad+U9iXEVfjtKBEbqWnm\nt5L+M3JPUP5Zyv+1WCIs2ZQ9Rvdf0P81aj7MpD+iLLwTMLiP0/+Vzkdo+VVm/SFlV6+A2jXAv2Y/\nVcsHgfNBUYfAuaCovRgC+NmgqC0oag2KzgYFFWJmxeJmxhNmx+LmxhLmxBPmxOJmxRKS72DTyQuc\nknVIxoERT+tRsETScuVWSFouaaEy5RNE3xctEDgtZbd+e/TbrV+HjOVqrFZrjTor1Kq4AsD3ydjt\ngl0ueMMFw3LWmGyNZmtN1jxBFJ+Rt99Zu7TarRWsMctasy0x7bJNYdCwfY7Y7bBjWs01w0qLrLRQ\nzaikKnTpiED+DTkZS6y1zFpTzBjTJdvttCNeccyrKtVb6BbzbVQxSpc+pctpzzrtaYGi2e4xy50q\nRjVsDTjonIdd8LRaq0zzQY1uHBlEktOhzzf1+oZS09X7lBr3i0dAXnBCyl/L+JpSt0j6DaVuCcsu\ngzy5h0n/OcUzlP+rsLQyHmnzpF6j+08Y3kz952j4bUqikYl9r3Dq/6V/CzP+FdN/g9JLU7auVrsG\n+NfsbVsxCPQL9AeBXoHuoKgnCNdugc6g6EIQuBAUdQZFHUFRj8AkMVNjcVNicS2xuOnxRLhGPiOW\nUP0T3EUUBE7LOSrjqKzDMg7JOC5rshKLlFum3FLllkiarXRC7ny09cvZb8BeA/bqt8+ASgmr1Fql\n1kq1Fqi+YoJ2QNY+nXbrtNsF5wxZoclqzVZrNmcCEbNQS6bPHmfs1uqwDnM1WWWmNWZpUX9ZvqBT\nr70O2+uIs85bZLZVFltm/hi6Brqcd9AbDtolZcgSqy21VotZI3x6eO0XHPOao16Rk7HATRa4UcOo\nJG1BVrvXnPK0bgdNd7PZ7tZo6agk7aDznnTOD+T0m+r9pnpA+Ui0XjTsFb2+ZsjLar1fvU9JWjry\neM4zUr4kb5ukT0n6nESkphkU+8j8DZm/JD6D5L+m9CGxWAlBgcEf0v2n5Nto+D3qP0u8Oiy77Ho0\nBPpMWxjNT/ssiQoKGU58hRkPkZz8pr+Rn2e7BvjvMisGgTmpblWxmBoxNdFaGYupiFpGKmMxSTFl\nwnF4pSiNYqY4I6vwyw0nWQkpnbxQoCt38TgIpAQySAWBtMCwUPxrSGAwCAxGID8oUC2mNhZTL6Yx\nFtcQi1YxzbG45lhMUyyuORY3ORbXJDbh0I53Yn0Kjss6ITuyHpV1UlazEguUWaDMYuUWKbdQ+YRK\nkuMtpeCwQfsNjHi3nCWqrVBrhRrL1UxYRXPR+mXs02WPTntc0GbIEo1WabJKs4UaJiyzTMnar80e\nZ+xxRl7RKjOsNMMKM1SOkz8oCrRqt89R+xzRb8gKC62w0EKzlY2r1+/S4aBdDnpDypBFVllijZnm\njgH5lH4nvO6oV/VqN9cGC91kyqgu2YuUzSnPaPOSOvPNdpcWNymJNpdAoM8bzvmhLi9osMFUD2mw\nYSSaz+vW5zt6fV1cUr1PqvWQRFRFVNQr42tS/peYKhV+TbmPXGqUKhwi/Zdkv07p/SR/V6xkQ/QB\nDdH39yF1k2ii8Q+o+SCxEooZOr4RcvTxJLP+iOZ/QbyE3ABH/4pDf07DGtb9D2oWvOVv5+fVrgH+\nu8yCKHoeCAIDo9bhCJiHhcCcEsgLOf2sEMSLwkRs8aIHgXgs/N82FnkpEi5uEmHnaRIVYsqj4yox\n1bHYmLU22njeTAL4J7WswDk5ZyJvlXNKzilZp2TlME+ZucrMVWqeMvOVm69MxdsAduiTc9SQwwYd\nNOiQQW3S5qm0TI2laixTY47KK/L3gcB5w/brtl+XvTqdN2ypRis0WanZIg2XiZcR1safcME+Z+11\nxmnd5ptshelWm2m6hsui+LSMw0464Lh9jqqUtNxCyy0wR8sYCYRAoMMZh+1x2G5paYutssRqM8aB\nfMaQU3Y4botzjphltfluNMPKEV4eBrVp9bxWzyJmlrvMcrtKk0edq0OHx3R4VEzcVA+a7D5lI7Nl\ni4a9ps83DXpOtXs0+KSktaPuCHZK+VtZDyt1lwq/psQNEW1TJPcYmc+T30H550j+ulg8uuvItdLz\nBfr+hopNNP4+FTeFpZW5bs7+NWf+kuoVzPo3NNwZPpbu4PDnOfpFpt7F0n8XAv5VbtcA/5r9VC2t\n6Ly88/I65LXLOyenPTpuk9OtoFnCdKVmKDVTqdnKzI7WSRJXLIEcbzlFp6QcM+SYIUcMOWrQoIIF\nqixUZbFqS9SYp3JCcL507XnH9Dqkx35dDugCS02yzCQrTDJf/ZjhHxetqOiULge026/NYedMVmO5\n6ZabbrFpysdV/oTUTqcDjjvgmFbnzNZiqXmWW6jZWI65oKDVMUfsdcReCQkLrbTYqsvomrRBp+xw\nwuvOOWK6Zea63mxrlY4RP+t2xgtaPW/YedPdapbbNVg88h0UpHR6XocfG3RQkztM8T61Vo48J6dd\nn+/o8y1xVep8TJ0PjtTOBwZlfEfa3ynqlvQZSZ8RjzaToNhJ5u/J/BWxBpK/TdnHxWLJsBU99SI9\nf8nQs9T9YsjPX0zEDh+h9b/T8TWaPsDM36cmGlvYf5CDf8aZ7zDrYyz+gzCiDwJan2bKDZRfylNc\nbXYN8K/Z27ZAYFigX0Gvgp7Iu6O1S16nggvyuqI1LdAsYbISk5WYptS0cetUJVfkxK9kGUWnDDs5\nyo8Z1i5tmqR5Ks2PAH6hKlMl35S/LwicMeCwHod0O6TbGYNmqbFYYwTyjSarnHDzKUQAf0i7A9od\ndk69Ssu0WKrFEtPGSAxftCEph510yAkHnRAXs9R8S82z0OwxNfKEzVDHHXTEXscdNMlkCyy30ApN\npo65tpR+J213wlbnHdViuXmuN8uaMfXyWQPOetkZL+h11DQ3mOk2zdaMVNkECnptd97juryg1kpT\nvE+jW0bq5ovSBj2tz7ek7FLrAXU+JjlqI8jbKe3vZXxfqZsl/YpSd4hJhLIHhddJf4HcDyl9kORv\nktgQVmIVh+n/Bj2fJ0jR8DvUfppETQjYPc/S+hdhIrblV5nxW5S3RMOQX+Dgn9K1hYW/xYLfINlM\nMc+Rb7P9v1LMcd83mbTiHfwSf77sGuC/yywQ+G1tKsRViakQVymuXCzy8Lg0Gu+QEFMSxXIXAS02\ncq4QyMLa+0Ax4u6zgojHD2QUpYUUUUpRWtGQwJCCAUVDkfcr6ldQKqZOQp2EhnHeJGGSEk0SmpRo\nVqJe/G1H5+OtIHBexhkpp6SclnLasNNSOmW1SJqj0hyV5qo0T6XZKieseR9tRYE2g47qdUSPw3oc\n16dBuYUaLNZosQbz1Su7QvVNVt4JFxxyzmHnHHVegypLTLPEVItNu6wunlDA7KSzDjvpsJPO6TTP\nTEvMtcRczRov+7y6nXfEPsfsd06rmeZHxM7yMdOiYFCXk7Y7abtOJ8200lzXm2nVmEg+Z1i715zx\ngk57TbHODJtMtUFiVM5i0BHnPe68J5RpNNl9JrtnVDllIGOvXt8x4IfKLVPnI2rcOyJJXNQn49vS\nvizQK+kzyn1KQlgxEwQDZL4eRvNBP+W/QflnxeLRIJLsCXq/EHL0yRvDaL7qbmJxCik6vh5G9ArM\n+NdM/SSJyhDAT3+bQ39KfpDFv8ecz1BSQW6I/X/Pzj+lehbX/RFz7gvPeRXbNcB/l1lR4FEDUhHQ\nDkdAnInAOSuQEcgKFCIeP1zDz2P8pxKPNoZ4lDorFVMWeWnkleIqxCTFJcVUiY94dbTWSaiVUPYT\ngveVbFBem7R2aW2Rn5V2Rso5GbVKzFRhlgqzVEZrhemSEyZDx1tOwSn9jutzXJ9jeh3Xp06Z+eot\n0GCRBgvUX6YTP9oGpB3REfk5p3RpUW+RqRabapGpl4mREX6f7c474pQjTjmm1WSNFpljsTnmmjEy\n+emi5eW0Ouao/Y47IC9nvmUWWG62hUrHXWevthGQ79dhlrXmuM4MK0dUKcPzprR73RkvuGCXJivM\nsMk0G5WO2pzSzkXjzp9QMGSye0x2n6pR4md55/X5gX7fVTSs1ofU+bCyEbniQN4r0r4i68dK3SHp\n01E0HyWD87vIfInsNym5jeSvU3JXKHsQFBl6MgT61CvU/RL1v0lZdA3pM5z9Am1/Q+0GZvwujZEs\nQraXY/+Lw1ECdvEf0HJ/CObDHez6PHu/RMutrPs3TAtlGJzZxuRllF2+UV8tdg3wr9lPxQKBfnkX\nZHXKOB+tHZGfj9a8QIukFknTonW6pJkqtEhKXiHCHm8FgQ5DTukf8ZP6tRs0TbV56sxVZ4F6898C\n3PMKTut23HnHnHfMBX2GzTfZQlMsNMV8k1VMcI6iwDkXHNPqqNOOOa1S0kJzLDTbQrNVjdsYwiqY\n80445IRDWh0zWYt5lppvmclaxkT9RXnnHIlasXYqyJplrbnWm2aJ+KgNJGvAOa876xUX7DLJ0hGQ\nLxulsZPRqdNzLnjSsJOa3GGy96qzepSm/bABT+r3Ayk71LhXnQ+rsGHkOQVnZHxDxtcRl/RLyn1c\nPNK9D4J+Mv8YllUGbZT/S8r/5aUkbP5CqG/T+yXiNTT8FrWfIF4VUjO9L3D2f9L9NFM/xYzfudQZ\n23eAI5/n1NdpeR+Lf5/GdeFjXfvY+ecc+y6LPs7a36d+IcUiRx7npT+h6wi/+COmrX5bv7mfR7sG\n+NfsbVlW0YC8fnkDcvrk9cqNeI+cblnd0dorp0JCszJNyjUp06TMFOWmKDc5WmuVvCPKJ6ug3ZBW\nA07r12pAqwFnDapVZo5as9Sao9bs6PhKtAwXO0l7ndDphAtO6NSq2xS15mk232TzNJuhYUxVzEUr\nKDjrvONaHdPquFZVKswz03yzLDRLvcuTgMMGnXLESYedcAiBORaba7E5Fo1RoYS0Aa12O+0NZ+1V\nozlqxVprktnjuPtu7V7V5lXdDmi2WoubTXP9GJDP6olA/ilDjmh0s2Z3abBRPCrzDOQNeVG/hw16\nRoXr1HpIjXvEo7uCwJCMR2R8Xd4byn1IuV9QYkNUaROQf4XM35L7PiV3UP4rlN4rFkuEQD68mb6/\nZvAxah6i/tdJXh9G7Pl+zv1DGNEHQdgkNe0zlNRSLND+GEf+kt5dzP8cC36dipbwLuHU4+z8C7r2\nsPI3Qq9sJpdm19d4+c9IlHHLH7LyoyQul6O+muwa4L/LLBD4SyeUiUuKR5x9XKl4xNvHo5r7mFhE\n08Si+CoY8fCzucjdh5RPUT7i7bOKI55WlFaQUpBWlFIwrGBIwZC8QQWD8vICtUrUKlGjRK1SDUrV\nj3iJRmUalZmkVIOyt+TSr2R5RR2GtRnUbkibQWcjUO+SNlmlmWou88oJtOPHn7dNj1O6nNTpZATu\ndSrM1WyuJnM1m6NJ8grnSss4pd0JrY4747R2jerMM8N8s8wzQ904dUrIyjjjRMTcH9any0zzzbbQ\nPEs0mjwGtANFnU5ptUurXXq0abHMLKvNtFrVuIqdAWe0eVW7Vw04Y4rrTHezKdaP1MqH19Gt0/M6\nPWPAQY1u1OxujTaOdLcGilK26/dDA36s1Cx1HlLjfUouatYoynlRxtdl/ViJ6yV9Upn7xS7W5hfb\nyXyVzN8hTvkvU/5psfiU6Au5QN9X6P1r4uXUfY66T5GI/rbB3Zz9Ih3/SONdTP9N6t8T0TY9HP87\njnyBsgYW/Q6zPk6iPOTnD3yVXf89bKpa+3ss/Bgl5QxdYMsX2fIFpq3l1j9k3h3hOY+/zvTllI/d\nbK8muwb47zIrCnzNGRnFEU8ryEegnYv4+rxAECVkgwjUYxFkXPw241FCtyTaIErElP7/7d13lFzV\nmTb63+nuquqsbnWrlSNRCBA5m5wE2GCCCcYmGYMxHs8X7nwzd2Ytz/fN3DvjuR7bY5IBYzImmiiS\nyDlKIgoQyrHV6pyrqvvcP/ZRqxWwAWML5H603rVPhVO1j6rr2W89+w3JApIeZCUKlShQrFCJQmUD\nVjQwlvwJm68bo0+sWbd63dboUq/Tap3qk+NGPWqUGKPMaGVGKzdOubEqjFT6qbT7Tr2WabJEo6WJ\nrdKiRoVJakxSa6JaE9VsUo9mHWKxRi2WWGmRFRZZbq1mY400xTiTEyvdTPRNXt5KixPlfr56K4w0\nNlHutzfahA2qTxK8+BXes8xblntHWpnxdjXedKPtoHCDrlR9Gn1gVVIlP6/bGPsZbX8j7DLgoUOv\nBo2e0eApHT4y3AFGOEK1/QYibMLm63vaPKjNQwqUqXSiSl+XTjJcw3V9oNftet0hMlyxM2WcpmBd\nFm2cJfdQCKnMv0D6VNLnU7RfiLSJ++l6kpZrg0ZffhLVF1G8XyDdvm7W3MWKX9O7jDHfZ8wFIdoG\nmt9i/hUsu4sxJ7D9pQxPfgm0LQ76/Lwbgj6/298y9uDwWMMHvPhL3rmDaadw4H9j5LQg6bw9k0d/\nxtol/PgBxu/6R/++vqoYIvwhfKHoltesR7NeTbo16tGo29rEGnRr0q1SRp1SI5QYpcwoZUYqNUqZ\nEX8kPn7D98tapdVKzZZrtlyTZZp1yxqn2gQ1iQ033vANWvltjE7dllltqZWWJJZSZIIxJhtrsnHG\nGqloMxJRTtZKSyyzwFILrLJUrVEm2tZE2xlrsvRGC0u/vDUWWO5dy72jxUqj7GC86cbbVaUNU/yz\nOqwxx2qvW+01JWqNtq/R9lNl241knRUaPWOtZ3RZbLgD1DpctX03IPmsj7SZqc2DyKtwgkonKrbj\nwGv1WSXrbj3uFKuXcWoi2YTwxRBOOTvUnc/+jsKdyZxD+lRRlJRpzi2l9SZar6OgiqoLqTyLwqrk\nP38eK68N0k3FXoy9mJrjQzZsXy/Lfx+IvnNJItt8n+KRQeJZ8Sxv/SqMU89j1x8ybHJ47ONZvPRL\nVrzJPhex3w8pH0m2m5dv5fGfkyphxv/FXqdS+MlVUbcGDBH+EDaLfrEeeZ1yOhJrl9Uhq11Wm6wW\nvVoHLKtFjxjVMqoVq1asRrEaJWqVqFGiLjneuADYH5tLk06rtVit1WqtVmqxUosOvUYZZowq41Qb\nb7hxqtVspsn3YHTqtly95VZbZrVlVunUbZyRJhhtojEmGrNZ/Z2gwS+3KLGFGqwywmjjTTHBtsaa\nrHiTzdl+TZZZ4X0rvW+1j1SqM9bOxtnFKNtt5MXH2iy22hvqva7FAjWmGWUvo+yrLPGq1712u3ka\nPa/Rc3Ka1DhYrUNV2XuQJh88+XaPaPeIfr0qzFDpBMWmDywa/dbq9YCsu+W9K+04GWdI+dpAqYS4\nb3Eoc9B7C3pIfzdINoVJJE1/F+33hk3YntlUnhaIPrNH4s13BW9+5bV0Lwy6/JgLKUnOb/84RNss\nup6qXUPs/NgTwyLQ28YHN/H2leG1dv0hO36XdDm9Hcy9mZcvC8894MdM/zapYlpW8dSVPHsNk/bi\nmP/B1MPC+739NNvtTemmktzWgiHC/5IhFrvG24oUSCtMtPsChQoUipLwymhQzP362Pv+JNY+HnSc\n05/o9/1y+mX1yerTqy/R8ft0y+uW15OMXfK65WQUKVWkTEqF9CY2TNowmQGrllHyGTdh1yGvX6MO\nDdqt0aZemzVak7FNmYxRhg3YGFXGqPqjxB4iYFqttMYKa6xQb7l6PXqNVWdsQvDjjVJr+GZfq1+/\ntVZbabHlFltpsU7txpqU+P2TjTZhEw8+Fmux0irzrDTPKh9IKzXWNGOSlKzijfT+rHZrzFXvTfXe\nVChlpD2Nso9au2ygx/fp0eINjZ7X5EWFStU4WI2DVZq2npj16zFXu0e1ewSRCjNUmLERybfIekiv\ne+S9JuUoGSdLO3qQLt9E9m6yt9D3PunTSJ9N0QGJZBPT/WLQ5tvvoWTfEFJZ/g0KSpKGza+z8rpA\n9sMOCCRfcxwFKfqyrLiPBdeETdhJ5wSPvnL7cNFr3+adq/jodsYfFYh+nWyzdn7Q5ufcxORD2P9v\nwhhFLJ7NrF8y90H2O4sj/4bRO5DL8vwd3Ptzcr38/Z1MGkq82uCcLU22WzPh94s9YIFcQsg5fXL6\n9SU6fX9y3D8o4n7dZu265KuCRM0vSDT7lAJFyYKRViijUDqxjEIligasOCH5Uqk/WBP+s6JXXrNO\njTqs1ZGM7Rp1WKNdqy5VSo1QoU6lOpVGqjTSMHUqNhsCuTG69VhlrdUarNJgpTVWapCRMkadMeqM\nM8pYI9UkKWGbQ6d2Ky2xylIrLLbaMqUqEoIPVmvUJlE76wn+gwErlDLGVKNNNcZU5UnC0jr0y2v2\nYVIhf7Y2S9Ta2Uh7GWlP5Umbv/X/j/WavKTRC1rNVm5Hwx2oxteUmjhoLjldXtPuUR0eU2CYCseo\nMENmUA/Zfq2yHk5I/iUpB8s4VdqxoqRrVhx3k30wePP5pyk6mszZpGaIouRzyS6i7aYg20QZhn2X\nyu+QSsItsw2svoVVv6W/m9HnB48+kzzePp8Fv2HxjVRODSQ/7uSwCZvv4eO7A9G3LWHnC5l2IeVj\n1odVvnwZK99kzwvY9wdUTaAvz+x7mfVfNC7liEs55ELKqmlv4pGreehyxu/EN/87exxDwVDi1Sbn\nbGmy3ZoJ/6uGXnlturXp1qJrE2vSqUmnrLxqpWqUq1GuVoUaZWpUqFNhuPJPtRlLIPZ6jeqttVqj\n1daqt1anbqPUGm3EgI1Rt0Hjj03n32O15VZbapWlVlmmR7cxA8LOBGNMVLpRy0BCP9dGS9X7yGof\nWeUDKcVGD+Tb7qjShs00YrEOy60x1xpzrPWOUiONtKc6u6sxbZPN2Xbva/SCJi/qVa/afmocpNp+\nUoMybft16vCcDrN0eEraRBWOUe4YGdsMel6LrEdk3SvnRSkHSTtZ2gwFiYQVxzlyT4SkqNwDFO5N\n5izSJ4uiRObqa6H9LlpvJvs+FWcw7ByK9wpedX+epkdYdX0oe1Dz9bABW3VwkiXbw/J7gzff+j6T\nv8uU71G5Q3j9lvm8e23YhB2xO7tczOSvB5mmq4k3f8trV1FcHbT5Xc8IenxHI8/+hqeuoHZS8Ob3\nOCno88s/5P5f8uzt7HciJ/03pkwPnv6sOzlgBlUbLspbE4YI/68coWVcnx65AeuSTaxXl6xOvTr1\n6tCrQ8/A2KZHn36VSlQqVqVUlVLDlKpOjocrN1yZcpnPGG+f06jFWs3WarZGkwZN1mjSK6tOjVFq\njDLCSDWJIPPJXjtBd68fEHVWqLdCuxZ1xhhlvNEmGG2C4Wo3KDy2Dr06k1Ssj9Wbb42FygxP8my3\nN9qOm3jwof7Qag3esdbb1nhLpECd3ZM2KNMVbxRi2ates1cTe01GneEOMNyBKu2c5E4H5KzU4Skd\nntLtNcV2V+Fo5Y6USkoXQL8GWTP1elDeK1K+Ju2khOSTZuJxnvwzZO8key+F25E+g/RpooLktfp7\n6HwkdI/qfIKyI6k8m/LjiNJBsul4K2y+1t8W9PjR51H3rRA3H8c0zwm6cBmh2QAAIABJREFU/NLb\nqdqdbS4M2nxhmnwvC+8NRN/4DlPPYefvhySpOGb5a7x2Ne/fy44nsN+ljEuidBa9EfT52fey+4mB\n6CftEX4FzH6cB3/Fx29y7EUcfwnDR9HSyL3XcPcVTNiBv7+Kidt/6r/TrxqGCP9Lhljs5x5TOCDD\nFChSOCDTRChIaG1wzH2cyDz9Yn36B8acPnl9iTQUrFdeNrFeOZFIsZRiKSXSSqSUyiiVHrByxcpl\nBsYKxSqUKJH6XJp9v1ibDs1aNWrRlIzrrEOX4arUqlKrWp3hRhiuznDDVPzB9+zTp8maRNAJws4a\nq+T0Jqr9WCONM9JYNUZuEh4Z5ten2YqBXNs1PtapSa3J6myT5Ntuu4kGH4t1WmWtd5MK+W+L9am1\ni1q7qDNd2UaZs326tZqt2WuavSZrrWr7qLavavsONA4Jr9+n21ydntLhSXn1yhyq3GHKHKJwkMff\nZ6FeD8l6SJ/3pRwh4xtSjlaQzDuOc0Gmyd5N9j4KJpL+ViD5wknJm+bpfDIULut4IPSBrTyLilPW\nx8z3LA/VKVffTF8HI89m1HcoS7z1njUsuZWF15NvZ/K5QZ8vT96j8V3eu44Pb6V2OtO+x5STQux8\nTytzb+X1a8i2s/f32eM8yutCtM1rd/L0lbTWc9jFfO0CKkfQ2coTN/DQFZSUc8KlHHImmRIWvs8d\nv2LWHRxyEmf8mB2GyiNv9pwtTbZbO+HPtVRfstG6bowH4u7Xj5H1W7brFoJCkcJkSVi3WKQSCxvB\nRTKKpBPLKNpsmOGfeg2duhNCb9OqXYt2Ldo0J9aiXali1SrVqBqw4YapVa1KxWYzWwejX78WjdZa\nPaDcr7Vas7UqVRthdKLcB6vcTM35dfNtt0ZDkmvbYKFGS5SpNsIUdbZRZ1vDjR+oHrn+3D5tllrr\nXY3es9a7iNTa2Qi7qrWLcmM3SqrKazdPs9e1eF27eSpMVW0fVfZRYceBDVfIa9TpOZ2e1uE5KaOU\nO1yZI5TYbYPN2bzZsh6WNVO/tTKOl3aClEMM9H+Ne8k9SfaeINcUbJPEy586iOT76H6BtjvC5mtq\ncihxUHEaqWRfId/KmnsC0bfPCU1FRn2HqoMSySbLyoeCLr/m2eDFTz6PukTS6W1j/u2B6DtWsNO5\n7HQ+w6as9+Zfv5b37mHbI9n7opAkVVDA6vk8czUv3sjkvTjsB0w/noJClr4fSP7Z37HH0Xz9R0w9\nILzmS49w+38x/21OuZiTL6Z2FKtXcNOVnPV9xq3fC9naMET4Q/hU6NevS49O3Tp16dClXWdi4bhN\nR2KdMlIqlatSqUqFYSpUqVCtUrVhqlVK+XQxz1m9A4JOozWarLFWvWYNylSoNUqNkYlqH443LjC2\nDuvIfa0lSa7tImstViQzkGtbZ4pak2VsmnGZ16PZfI3e1+g9TebJGKbGNLVJG5RSIzfJmu20QIs3\ntHhDq7mKjVJlb1X2UmUPhRs0GM/r9pZOz+r0rKyFSh0w4MUPlmpi3XKeSTT5R0SGSTte2nFJaYOk\nUFncFRp8Z+8h9zCF00ifTOpkUWFCcHF/6APbfkfQ5gvrqDydim+RTvYA+ntpfJjVt9I0i+rDQ02b\nmuMpTGrVN73O4puDZDNs5+DJjz+FVFLGeMVzvP9bFt7P+COYdgETjglk3d3C3Ft441qynez1PfY4\nl4pR5HMhyuaZX7N0Lgedx6EXUTclbNC+cn8g+mXzOOZCjruYmjF0tPHQDdx5GWWVwZs/6nTSGd55\nk9/8gqcf5qRv88N/YOSGG+VbE4YIfytFnET05OQTSSefWE6vnKycrKxeOb16devVI6tHr249uvXo\n2mgsllGmVLlSZUpUKFOhVIUy5cpUKjdMuUrln5rM16FXjxaNWjVptlaTNYl636Bbl2q1atQlok6d\nWiMNV7dJKORg9MlpsXJQru1SjZZIKVZrklqT1JhohMlKk8YcG/8fdqlPquPP02iedktVmqjGtMSm\nbqLBhy5Pi7SYrdUbWsxRpEKVPROS31N6UKNvyFqmyws6E0sZo8whyhyi1J6iQQtYnxVyHtPrEXkv\nKjRd2gwZxym0vj1f3N9IbmbQ4/NPhY3X9CmkT1qvyQ+Q/F203x0KllWeTsXpZJLkq/48Lc+GNoEN\n91K+CyO/Td2p6xt/dywOks3im8Ovg0nfCVY+OTzevpQPbg4liYtKgie/w7cprQuLwOLneeM3fPAg\n2x3D3hcy+bDgza9dwvPX8dxvGLFNIPm9Tw1x9Y0rmfXbEHEzchLH/5ADTiaVZvEH3HUFj97KPkdx\n+o+YfiB9fTx+P9f/F8sXc86POPNChm36N7C1YYjwv2SIxf7ezxUkskxBouPbSL7BIKEnkHt/IgH1\n6dOnPwnLTCWyTpBu0lLS0tJSMslxsYziQWOJYqWKNxpLNtvZ6dNeU69ubVq0atKmWavmgeMWjfJy\nhhlumOGq1SaK/QjVRqhQ9QflnX792jUkebbLB8Z2a1SqM9x4NSYabrxak5R8QjJVj5aBCvlNSSuU\nAinVtldjquGmqrbtBvXiw/vndPhAq7lavaXNW4pUGma3hOT33ECHJ8g0XV7R5UWdXtSvU5kDlTpI\nmYOlNtDts3JeljNL1iz9Vks7UtqxUo5UMGjBifs+CiGUuQdDS8DUEaS/SeoEUUGyyMQ5up4LSVEd\n91JQTcWpITEqM23dC9HyfIiVb7iHzHhGnkHd6RSPS/7DGkKJgyW3hU5SE05j0nepScok9LaFcMoP\nbqbxbbb7FjtdQN2e4fGWZSFmfvb1FBWz5/ns/h3KRpDPMueBQPQLXwux84ddHGrd9Pcz9wke/nVI\nlvrat8Im7JTp5PM89wB3X8mCdznpe5zyA+rG0rSW313LLVcxejzn/5hjTxYXFMg9/pjey3+l5F//\nTdFuW6+WP0T4XzLEyde7P9l47U8IfP3W7PpnRsmisO5fQaLZFw4sE19s7frNIatXl3Yd2hNBp3Vg\nbB9Q71sVKFChKhF0hieiTjiuUqNU+R/d/M3LarMmybEN1mylVquVqExybMcNjMOM2qAe/GAEcv9Y\niwUJyc+X163KNkkLlO1V215JUixsMHLatHl7wNp9oMQ4w+xmmN1Umi6zUThmn1ZdXtflJV1ekrNC\nib2VOUCpg2QGtRAMz18g6yk5T8h5QaHtpRwl7UhF9lyv28e5UIky9xDZB4g7SJ9A6gRSR4qiJNu3\nv5vOWYHgOx4Mmnz5N6k4eb0nvwHJ/570aOpOC1aa/HLItbH8fpbextqXGX0cE89i1NEhyqYvx7JZ\ngeQXP8K4Q0MG7KTjwwZstot59zH7hlDuYJdvBaIfm4RyrpzHc9fx8s2MnsrBF7DnKWRKaVodNmEf\nu5bSyiDZHHJWyIxds4L7rg02dkog+cNPCbLN229w0xU8dh/HfJNzLmWXPcQdHXpvulHPlZeJiksU\n/+jH0qefISretDbS1oIhwh8C1oVnZjcQdLp1DYzdOnTp1KVTtw6diYrfr1+p8kTIGSzqhOOg4FfJ\nbKbA2ObQr1+HRm1WJ3m2oZhCi9W6NKtQa5jRqoxRbWySbztG6hMLoPXrUp+0PVk0QPJ9elTZxjDb\nJC1QtlNm9CaLTjh/cULu72jzrqw1Kuyk0q4qTVdpZ0Ubxen3adXtDV1e0ellWQuV2E2pA5XZP2n7\ntz7evl+LnOfkPC3rSXRLOVzakVIOUzBo4Yn7G0Jj79xMcrMomELqeNLfoHD30EAE+hrpmEn7faFg\nWfEeCcmfRCopiLZOrmm4O8g16dEhhHIwyee7WPUwS35H/ROMODiQ/NhvUJTUqa9/nQ9v4aM7GLZN\nkGu2P52S2vD4kheZc2PYgB23b9Dlp34jxM13t/P6nYHoGxdzwDl87XxGJfXq58zi0Wt46ykOOjXo\n89vvHV739Se5+ypmP8PRZ4aN2G13oaeHh+/ixstZW8/ZP+D0Cxheq2/BAj1XXSF7842KDjlU8Y9+\nrOigr4m7u0XFxaKtOPlqiPC/hPjAWwMe+zrfPWCwf79exokH5JwQ0xNU+z598olqn5OXTY56ZWUT\n5b43Ue2Del+gUEaxEqWJmFM6IOoE5b5cSaLir1Pt058xvh6yurRr0G6tdg3arEkKKqzRoVGxCsOM\nSvJsRxlmpGFGqzRig+YeGyOnS5vFWi3WZpFWi7VaJKU0aX8yJWl/su0mG6vr59aozbvavZfYPCnV\nKu2s0i4q7aLMNhvEwhMkmm6v6/KqLq/KWqzE7krtp9R+iu06UH44fH698l6X9bScp/T5QJF9pRwm\n7UiFg7Jh47ifvjfIPhw2XPs/pOiIxJOfsV6Ph+yCEDrZ8UCoX1N6RCD48uMpTHIE+ntDItSa37P2\nfoonBj1+xCnrSb6vh9WPs/QOVs4MFSknnsG4b4ZyxND8UQij/PC2cHvH7wSir0o2eJsWMudm5t4U\nMmb3OIfpZzNsbCDr+S/w/G+ZfR87HhrCKXc5NiRIrV3OrOuDPl9ezYyLQkhlaSXNDWET9vdXh3DL\nU3/AMWdRVsGyxdx2NXf+lp12C978YceJCwrkn5il54rL5F99Rebc82UuvkThxImyy5ZpvOIKTddd\nZ/LMmUr32efT/il/5TBE+F8yxGL3umGDAMwQgrkO62vnrAvALEgWhcJE0AljOE5JK5JKtPyUtIyU\njPSApWWUyCjZbDz6Z0VOj07NujTr1KxDY5Jr26RDkw5rxfpVGJHk29aqVDdQUKHCiE+UYda/R6d2\ny7RZOmhcoldr0vZkkmEmJeMUmU/Q7LOadPhQu3k6fKDdPP16VNhJhWkqTVNhmtRGG7pBdlug22zd\n3tDtTXlrlNhTqX2V2ifx4NODzsnJm5t48c/LezWRaQ6RcriU/Qbq1UDcvzJ477lZ5B6nYASp40jN\noOig9SUN4lxoAdgxk46H6Gum/OvByo4M9WsIse9Nj9JwX4iyKZvGiJODlUxKntMdSH7Z3SGcsmo6\nE05n/MmhMiVh83X+ncGT71geukftcBZ1iSTT1cg7d4XmIg0fhOzX3c9hbKLbr1nIy7fw0k1B4vna\n+ex/NsNGhmzX1x7k8d/ywcscfAbHfI9tk+SpN57m/t/w8qMhdv6Ui5m2T3jsmUe45dfMeYWTv8vZ\nFzNle/0tLbI33ajnmqtE6YziS/9G+owzKSnR9cIL1l52mY4nnlD93e+q+dGPZLZZn5G8NWKI8Ifw\nBxGknh492nRr16M9OW7TrVWX1oGxS7N+/cqSPNsy1crUKFOtXI0yw1WolfkUen2/nE71OqwY1P5k\nuXbL5XWrME6lCUnrkwkqTVBm1Abx6+uvoV+PVTrN1+HDxD7Sr0eZ7VWYqtyOKkxVvFHMPPRp0+Mt\n3eYMWKFyJfZUYi8l9pDZKHY+lpU3W84Lcl6U96oCE6QcLOVrUg7acLM17iD3XChnkJ9F/8qw4Vp0\nFKmj14dOQr4+dIbqfDjo8ultKJsRSL54r/WNuHuWs/bB4MW3vsSwAxlxErXfIJP8Ksi1B7lm2e9Z\n/RhVu4XN13EnU5I8p2MF8+8KRN/yUUiI2v4Mxh0WQimznSG6Zu6tLHme7Wew65lsdyxFabpaeP0u\nXro5aPT7nsEB32Hy3uH1F8wJ2vyzv2Pizhx9PgecQnEp9cuDN//Ab0NI5Unf49hvU1nNymXBk7/j\nuhBKedZFfP10SkrlZ8/W++srZe+9R+qYY2Uu+kGQbbq6NN96q8YrrtDf3a320ktVn3uugooKTU8/\nbdjeeyuqGKqWucE5W5pshwj/jyM0RcltkFMb8moHF1HoltUjq1NWd1JIoSspotCZFFDoVKgoyaut\nHDRWKjVMiWEDY5lqKSWfWuLJ6dKlXodVuqxO+luFHlfdGpWoVW6McmOT9ifjlRunRM0nvkdeh04L\ndfo4sfk6LVCoTLntlNteuR2U20Fms5p9Tq8PdZurx1zd3pKzQrGdldhdid0V232DKJpwXqec1+W8\nJO9FebMVmJKQ+4FSDlAwqOxCHGfJv07+yYTkZ1O0dyD51NEU7hna/xEyXbtfpvNROh4ltzB472XH\nUT6DolHJ8/ppn83ah2h8kO7F1B4fCH74MRQlRNa7lhUPhjo2a55hxIGMOyVo8sVJDf6OFXx8Dx/f\nFfrBTjkxRNmMPzK0Acxnmf8Yb/+Ojx5m/P7s9m2mnkimIjz+9iPBm3/vcXY6MpD8rseFRaC5nmdu\n48kbQkbskedyxDmMmpxUsHyQ+6/j3Vc44jROupCpe4aQymce4bZrePMlvnFmCKncabq4q0v2jtv1\nXPNr8Zp6mQsvkjnvAgUjR+qdP1/jVVdpvvFGZQcdpObSS5UfcYS+7m4rb7nFkssuI47tdscdKnYe\nqpa5wTlbmmy3ZsKPxe7zEwZF3wx+LE4KKqwvntCXKPj5RL8PBZH75BUolJLZKLc2BGCuK6SQSqLr\n1xdRKJFRLqMsKaJQtkExr89yHVltujQkfa0adGsY6GvVZY0+vUrVDeprNVqpUcqNUWbkBl2bNkaf\nbl0W67JIp4W6LNRpgZwWpSYrs40y2yq3nTLbbVBkbP0c+2Qt0ONt3d7R4229PpAyXonpik1XYrck\ngmbDufSrl/OKnJflvSLvA0V2lnKAlAMV2VfBICkojvvom0vuqRATn3sx1KpJHU7RkaQOEkWDEr2y\ni+l8LHSF6noqiaqZQdmxlOxHlMynrzM09G6cGYi+qJLar1NzQvDoC5K9hs4lLL8vkHzLHEYeGfT4\nMSeQTubZvowFvw/efNP7TPkG254WSL4oE5KbFj0Tuka993vqdmL6Wex8agil7O/n45d45VZev5sx\nU4Ncs/dpoUJlrpdXH+TJG3nv+VC87Ihz2eWQEG//8bs8+FseuYXJO3HiBSHSpriUpYuCJ3/X9YyZ\nEDJiT/gWpWX63n9fz7VXy952i6L9D5D5/sVSxxxLHGubOVPjlVfqmTtX9XnnqfnBD6QnTtS1cKGl\nV15p+Q03qD7oIBN/9CM1hx8eSjxvxRgi/C8ZYrG1Fm1QIyds1m64AKwLwiwYVFBhXQGFdePmCoB9\nEfPL6dCrRY9mPZoSa9Zt7aD+Vk0KpZWqU2JE0ttqhDJ1So1SaqSMYX/w10B4rybdlibkviQZF8tp\nUmK8UlOUmTJA8sXGfIKsk9XrYz3e1eM9vd7VY54iIxTbNSH4XWRMU7hRxE0sr897cl6T96qc18Ra\nFNlHyn5S9ldkD9GghieB4OeQezYUJMs/TzQm8eAPp+iQ9XHx0NcaGnl3zgpE399K2VGUHRPGdV48\ndH0cdPjGmUGqqdwnZLrWfp3S7dZNIBQpW3F/sO4VgdzHfZORR4XkJ2hdmHjy99A6n8nfYLuE5AvT\noUn4khd4+44QYTNsPLuezi6nhxLEsOI9XrktWLokkPx+Z4VKlXHMvJd46mZevJvJ04Mnf8DJYcO1\ntYnHb+fB62lcxfHn8PXzGL8tvb3Muj/Ezr83h2+ezRnfY4edxd3dsvfcrfc31+hbuCBswl5wocKJ\nE+VWr9Z03XWarr5aatw4NZdcYtipp4rSaWtnzbLk8su1vPKKceeea8IllyidPFnLhx96//LL7fy3\nf6tyK9bx/+KEH0XRqfhnTMXecRzPHvTYP+B85PHjOI4f/4TX2GoJ/y+FIPn0yg3qaZVNjkNPq3ZZ\nrQP9rXq16dWiV5simYGWJ8WGJ1Y9qK9VrWI1GzTr+OR59Mtq0G2FHiuScZnuxCKphNgnJTZRiUlK\njNkkUmbddeWt0euDQTZP1iIp4xWbNkDsxaYp3GhDN2yTL5b3ppw35M3W5x0FxiUEv48i+yq0/QYL\nahx3k3819HHNPU/fK0RjSR1G6lCKDl7fvJsQF9/9cgiX7HyS7Huhr2vZkZQdTWb6ei0+307z0zQ9\nRuOjoZNUzYxA8sOPCl495DupfypsuK58OJQ6GHtisNoDgt4exzTMYeF9obRB5+og12x7atDkC1PB\nk1/8LO/eE6pSltcFgt/lW9QkUTyr5/PaHbx2e9Do9zmD/b/NhN3C5uzSeTxza5BtUhkO/w6HnU3d\nhCDZvPQoD9/Eq7PY/1i+cT77HBk8/Xdnc+f1PHg7U6eHcMpjT6a4WH7OHL3XXyd7x+8U7bW3zIUX\nSR1/AoWFOp54QuPVV+t86inDTj1VzSWXKNl9d9m1ay2/4QbLfv1rhRUVJl56qTFnninKZCybOdP7\nl1+u8a237Hjhhab9+MdKRmyYQ7E1YUsQ/g7ox9X4n+sIP4qiqbgNe2McnsB2m2P2rZ3w73zml/Y/\ndMNsv/VRO+van/Qlkk5+wNb3sBrc16pHfmBc39Mqp1uhtCIl0sqlEksP6m+VUSmtQkqFYtUD/a0+\ni8QTZJNGver1WKXHKs8986Lph5bosVKvekXKFRur2DglA+N4JcZLfUKEDSEUstdHsj7Wa35C7h+K\nFMrYQcaOMqYqNlXadgo2WoACua+QN1venMRmi5Qosucg232ghPDAuf2ryb8YpJn8S/S9Q+EupA7y\nzItVDj3iYlHBoKSt/h56XqPraTqfpvdNMrtQengInSzZn4JkfnFf0OKbHg/1atrfpHLfoMPXHEPZ\nLoFUoWNhIPdVM2l4geF7M+b4YBU7JK0Es6F+zcL7gxVm2OaksPk6ar+wEOR7WfBU8OLn3U/1pNDs\ne9op1Ca/GtYs9Mx1/+7QnjdoWRmkmn1OZ9sDAlE3LOO52wPJt64JUTaHnc2U5G/5/deZeVOoUDlp\nR2Z8hyNPCxuwDfXcdyt330BHO6edyynnMH6S/uZm2d/dpvf668RNjdLnnCdzznnBm1+1SvP112v6\nzW8UVFWpuegiVWeeqaCiQstLL1l61VXWPPSQkSeeaPzFF6vabz89DQ0+vO46H1x9tdLRo0394Q9N\nOe00/f39Xnj5ZYcdfvin/vv+quHzEP6f1OU3juMPkzfe+E1PxO1xHOexOIqi+dgHr/4p7/dVxKxn\nHjLp0N5B94Ss2miDnlaDCyinRMnWaqHKpDli6GcV7ssM6mdVkvS0Ktmk8uNnRZ8eWY2yGhJSXyNr\njV4Neq1Jbq+VUiljlIw6xcaY80yzGYd+V7Exio1WuFHv18EIW88rZX0sa4GsBXotkPWxWF7G9tK2\nk7GtCsfI2F6RTT20WL8+C+S9NcjmokCRPRTZXbHvK7K7wkHFyQgbrHHf6+RfSexl4haKDghW+lOK\n9hrQ4J998Z8ddkQZnU8FmabrWXreIDM1EHzN31N6EAWDpKPuhUGLb36CpifJjGL40Uz4O6oPoTDR\n9/t6QvLTqkcC0edaGD0jVKHc/3bSycLU08xHv2PhAyx9jKodgiZ/4qMMnxoWgmwn79/H+7/nw4cZ\nOY2dvslh/xQIHxoW8fB/hMSoxqWeWTbBof/Pz9jxkLBQtDaEOjbP/o6l74Xomgt/wbSvUVjI8gX8\n5l949Jbw62LGd7j+VcZNCZLNEw8Gkn/jBY4+iZ/8F/sdIkb+6af0/t//KPfITKmjj1H6//67osOP\nII61P/qopr/5G53PPWfYaaeZcMcdSvbaS7611fKbbrLsmmv09/Yaf/HFpv7qV1LV1epfeskzZ59t\n2cMPm3TKKY685x61e+6pZckST//kJ+b89rdWnXjiVk34nwd/rrbuY/HyoNsrkvv+6jDWQfbxv/7i\n79uvV06bvFY5LXIDY4ucJlnNydgkq1G/rLSaxGpl1MmoU2aHgeOMOgUbxdVXaFLjoIHboaxvvZwl\nspbIWjRgOUsUGi5tGxnbythJhRNkbKfQiE8od9whb54+78gn1uc9kWpFpiuymxIXKbSbAqM23BiP\nY3H/IvKvBYmm71Xyb1E4maL9SR1JyT9RsMP6jFZC96fuh0ONmpZbmf//kdmV0kOo+V+UHEjhoF8r\n2XqaHwrk3vxkkHiqjwy9Xbf7xfrWf4Rm3qseDSTf8HyoQDnmOPa/jerdgvQTxzR/yOJrWfhgkG3G\nHRZI/uBfUpbsAXSuTTJe72XR0yHrddopHPszKpOFrv5jZv47b9wdWgPu8U1O+yk7HMK//CsT9uDJ\nm4I3/+Gr7HUcJ/9P9jwmyDfNDdzz61C0bPnHHH0G//vmEDMPc17lqp8x80523DV485ffTlm5vkWL\n9P7L/5a9+UbRsCqZc89X+ov/UlBbK7tokfp//mfNN9wgNXas6u99z/hbb1VQVqbl1Vd9fP756u+7\nz4hjjjH1l780/LDD5Do6fHzLLT749a/lu7pMveQSB1x+uXRVlUVPPumJk06y9PnnTT/nHOe/+KLL\nbr31c313tmb8UcKPomgWG8StrevX8Y9xHD/4Sadt5r6tV7fZwljlPvVmyuuU1yavTaxPkQopVYkN\nk1KtyDAlJqi0m7RqKcOl1ShS+bman6xDu8c0+E85SxWokDZRygRpU1T6hrTJ0iYp+AMtCgcj60kd\n/rt+qxTaQZFpiuwq7WRFdt4g7n1ziHuvo+sfUETRvhTtQ/pfQohkwaZRPuGkfpbsR3YexftQ8jVK\nD2O7qyjYtLyyuJ839g4efdXBobzw+L+lbKf1Ms065Np5dDf6uhl9LJPPYf9b1me6rkNfjtt2JdfB\n5BPY8+8Yf/j6jdl1eOInvPRLtj2KXU7j1Bso2ei1rjiVj15gz5M57T/Y4eCQ+boOi9/hvIlMP4Kj\nL+Aff0/xoOv8/TVc9ncceBwX/BP7HkXRIAnwlINoaghyzUNvblB7vvun/6bnF/8pfcZZyu+6V9Hu\nuw881vCf/2nNv/2bqm9/26SZM5XsuuvAY3PPOkvra68Z//3v2+GnP5WpC6GlrR9/7P699zbm8MPt\n87OfGXvEEQNlE26dMUPbihX2ufRSJ996q3TZZj6rIeALitKJouhp/I9BGv7fI47j+KfJ7UfxkziO\nN5F0oigaWgiGMIQhDOFz4C+q4W+EwW/8AG6NougXgpSzLV7b3EmfdcJDGMIQhjCEz4c/Kbg7iqKT\noihahv3wUBRFj0Acx+/jTryPh3HJVh2KM4QhDGEIXwFs8cSrIQwN1QI3AAADzElEQVRhCEMYwl8G\nW6xYdBRFp0ZR9G4URX1RFO0x6P6JURR1RVE0O7Ert9Qc/xR80vUlj/1DFEXzoyiaF0XR0Vtqjl8U\noij6SRRFywd9Zsdu6Tn9qYii6Ngoij6IouijKIr+8mFWf2ZEUbQ4iqK3oiiaE0XRZuXWrxKiKLou\niqL6KIreHnRfdRRFj0dR9GEURY9FUfQJu/VffnzC9X3m792W7A7wDr6JZzfz2MdxHO+R2CV/4Xl9\nUdjs9SVJad8SspNn4MrN5DF8FfHzQZ/Zo1t6Mn8KohCjeTmOwTScGUXRjlt2Vl84+nFoHMe7x3G8\nNRSNv174vAbj7/FEHMc74Cn8w198Vl8cNnd9fMbv3RYj/DiOP4zjeL7Nh3B+5QnwD1zfQFJaHMeL\nsS4p7auOr/xnNgj7YH4cx0viOM7hduFz25oQ2bIO3xeKOI5fQPNGd5+IG5PjG3HSX3RSXyA+4fr4\njN+7L+sHPimKojejKHo6iqKD/vjTv1IYi2WDbm8tSWk/jKJobhRFv/kq/3ROsPFntNzW8RkNRozH\noih6PYqiC7f0ZP5MqIvjuB7iOF7NZtK2v/r4TN+7P1emLT530tZKTIjjuDnRvu+LominOI47/pxz\n/Tz4a0pK+0PXiivxf+I4jqMo+lf8HBf85Wf5heEr+Rl9RhwQx/HqKIpGYFYURfMSL3IIXx185u/d\nn5Xw4zg+6nOck5P8dInjeHYURQuwPWb/wRO3AD7P9Qne4vhBt8cJi9yXGp/hWq/FJy12XxUsx4RB\nt78Sn9FnQeLxiuO4IYqiewUZa2sj/PooikbGcVwfRdEorNnSE/oiEcdxw6Cbn+p792WRdAY8qiiK\napNNM1EUTRGSthZuqYl9Qdg4Ke2MKIrSURRN9geS0r4qSL5M63Ay3t1Sc/mC8Dq2TSLG0jhD+Ny2\nCkRRVBpFUXlyXIajffU/M9a1h16PB3BucnwO7v9LT+gLxgbX93m+d39WD/8PIYqik3AZaoWkrblx\nHM/Awfg/URTl0IeL4jhu2VLz/Lz4pOuL4/j9KIrWJaXlbB1Jaf8RRdFuQuTHYly0ZafzpyGO474o\nii7F44JTdF0cx/O28LS+SIzEvUlZkyLc+kn9Kr4qiKLoNhyKmiiKluIn+HfcFUXR+ViK07bcDP80\nfML1HfZZv3dDiVdDGMIQhvBXgi+LpDOEIQxhCEP4M2OI8IcwhCEM4a8EQ4Q/hCEMYQh/JRgi/CEM\nYQhD+CvBEOEPYQhDGMJfCYYIfwhDGMIQ/kowRPhDGMIQhvBXgiHCH8IQhjCEvxL8/7rg06EnwmOU\nAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fc6d591b710>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "xmesh, ymesh = np.mgrid[-10:10:50j,-10:10:50j]\n",
        "phimesh = phi(np.array([xmesh, ymesh]))\n",
        "pt.axis(\"equal\")\n",
        "pt.contour(xmesh, ymesh, phimesh, 50)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Running Conjugate Gradients (\"CG\")\n",
        "\n",
        "Initialize the method:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "x0 = np.array([2, 2./5])\n",
        "#x0 = np.array([2, 1])\n",
        "\n",
        "iterates = [x0]\n",
        "gradients = [dphi(x0)]\n",
        "directions = [-dphi(x0)]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Evaluate this cell many times in-place:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "-4.61671051783\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fc6d5583dd8>]"
            ]
          },
          "execution_count": 78,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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9ekUxIaFks/rY2EL263edbdte5pUrpm+qkUpKSiGXLLlJD4899PY+zJ9+esC0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\nH6Jfe4Tr0yKRAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fc6d5671898>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = iterates[-1]\n",
        "s = directions[-1]\n",
        "\n",
        "def f1d(alpha):\n",
        "    return phi(x + alpha*s)\n",
        "\n",
        "alpha_opt = sopt.golden(f1d)\n",
        "next_x = x + alpha_opt*s\n",
        "\n",
        "g = dphi(next_x)\n",
        "last_g = gradients[-1]\n",
        "gradients.append(g)\n",
        "\n",
        "beta = np.dot(g, g)/np.dot(last_g, last_g)\n",
        "directions.append(-g + beta*directions[-1])\n",
        "\n",
        "print(phi(next_x))\n",
        "\n",
        "iterates.append(next_x)\n",
        "\n",
        "# plot function and iterates\n",
        "pt.axis(\"equal\")\n",
        "pt.contour(xmesh, ymesh, phimesh, 50)\n",
        "it_array = np.array(iterates)\n",
        "pt.plot(it_array.T[0], it_array.T[1], \"x-\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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      },
      "outputs": [],
      "source": []
    }
  ],
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